Programming in the teaching and learning cyclenumeracy4life.wikispaces.com/file/view/Exemplary+Stage+1... · Web viewIt is fundamental that all teaching is undertaken within the framework

Exemplary Stage 1 Mathematics Program

Programming in the teaching and learning cycle

It is fundamental that all teaching is undertaken within the framework of the teaching and learning cycle.

The following diagram demonstrates the teaching and learning cycle

Assessing: Where are the students now?

It is essential to determine where on the learning continuum the student is placed. Determining the location of the student against the learning continuum provides the teacher with information for developing an appropriate teaching program based on the needs of the students. There are a number of different types of assessments that can be used to determine the baseline level against the learning outcomes. The Schedule of Early Number of Assessment (SENA) from the Count Me In Too program or the Starting with Assessment (SWA) materials can be useful.

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The Teaching and Learning Cycle


Planning and programming: Where are the students going?

Outcome, Knowledge and SkillsThe mathematics outcomes plus knowledge and skills provide information for teachers on the types of skills and knowledge that is expected from the student at the appropriate stage.

OutcomesAre statements of the knowledge, skills and understandings expected to be gained, by the student at the end of the appropriate stage as a result of effective teaching and learning.

Knowledge and skillsA set of statements related to the knowledge and skills students need to understand and apply in order to achieve the outcome.The following is an example of an outcome and its knowledge and skills. The stage outcomes are also given, as the student should be making a progression between them.Strand: SPACE AND GEOMETRYOutcome: PositionSGS1.3 Represents the position of objects using models and drawings and describes using everyday language

SGS2.3 Uses simple maps and grids to represent position and follow routes

SGS3.3Uses a variety of mapping skills

• making simple models from memory, photographs, drawings or descriptions• describing the position of objects in models, photographs and drawings• drawing a sketch of a simple model• using the terms ‘left’ and ‘right’ to describe the position of objects in relation to themselves eg ‘The tree is on my right.’• describing the path from one location to another on a drawing• using drawings to represent the position of objects along a path

• describing the location of an object using more than one descriptor eg ‘The book is on the third shelf and second from the left.’• using a key or legend to locate specific objects• constructing simple maps and plans eg map of their bedroom• using given directions to follow a route on a simple map• drawing and describing a path or route on a simple map or plan• using coordinates on simple maps to describe position eg ‘The lion’s cage is at B3.’• plotting points at given coordinates• using a compass to find North and hence East, South and West• using an arrow to represent North on a map• determining the directions N, S, E and W, given one of the directions• using N, S, E and W to describe the location of an object on a simple map, given an arrow that represents North eg ‘The treasure is east of the cave.’

• finding a place on a map or in a directory, given its coordinates• using a given map to plan or show a routeeg route taken to get to the local park• drawing and labelling a grid on a map• recognising that the same location can be represented by maps or plans using different scales• using scale to calculate the distance between two points on a map• locating a place on a map which is a given direction from a town or landmark eg locating a town that is north-east of Broken Hill• drawing maps and plans from an aerial view

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When has a student reached an outcome?

When determining if a student is reaching an outcome there needs to be sufficient evidence achieving the knowledge and skills. There are three measures of indicating student achievement against a specific outcome. These three measures are: A student:Has achieved the outcome.Is still working towards the outcome. (Or progressing towards the outcome)Is achieving beyond the outcome (Student should be undertaking higher stage outcome)

Outcome achievedStudent can show proficiency with the specified knowledge and skills for the stage outcome.All knowledge and skills are met for stage outcome.

Working towards the outcome (Or progressing towards the outcome)Student cannot show proficiency with the specified knowledge and skills for the stage outcome.Student can complete some of the knowledge and skills for stage outcome.

Working beyond the outcomeStudent can show proficiency with the specified knowledge and skills for the stage outcome.All knowledge and skills are met for stage outcome.Student should be working on higher stage outcome knowledge and skills than their current stage.

When planning and programming to achieve the outcome it is important that a number of factors are considered.

For students with high support needs in numeracy it is necessary to:

break the content relevant to the outcome into a sequence of manageable skills or teaching steps

ensure the steps are carefully sequenced from easy to difficult or in a logical order. Some students may require very small steps

ensure that syllabus content is covered

clearly identify knowledge and skills that will show student achievement

identify monitoring procedures to check progress

determine the specific strategies and resources to be used

provide teaching and learning experiences to ensure that the students achieve the outcomes and move on.

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Factors in assessment diagram taken from Board of Studies Mathematics K-6 Sample Units of Work. Published 2003

In the programming process the teacher should ensure that the working mathematically strand is incorporated into the teaching of the other strands

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Teaching and learning experiences: How will the students get there?

Constructivism has played a key role in challenging the traditional view that mathematics is an external, objective truth that is transmitted by the rote learning of abstract concepts and symbols.

Constructivism encourages pedagogic approaches in which the individual has the opportunity to construct concepts and meaning by using concrete objects and other methods and by interacting with other students through pair or group work.

Lukin, A. and Ross, L.. (1997). The Numeracy handbook, Macquarie University

A mathematics session should embrace this constructivist philosophy to maximise the learning potential for students. There should be a focus on classroom activities that are stimulating and engaging for the student. The easiest way of destroying a child’s appreciation of mathematics is for the child to be forced to learn mathematics from a textbook only or endless chalk and talk. Children should be provided with rich tasks promoting investigation and problem solving. The structure of a well-planned mathematics session can be broken down into the following constituent components.

Warm UpsThe start of the session provides an opportunity for the teacher to review previously taught skills. Errors can be identified and corrected thus providing the teacher with information on student progress against specified indicators.

Main BodyThis part of the session is critical in the development of new skills or concepts.

ModelledWithin this session the teacher models the new skills and concepts. What is to be learned, how it is to be learned, and what students will be able to do is articulated.The new concept should be presented in small steps.Frequent checking of students’ understanding is essential.

Guided Practice:The teacher leads the student through some examples of the skill or concept.

Independent practice:The students practise the new skills or learn to use new information with a minimum of direct assistance from the teacher until the new information is merged with what is already known.

Lesson Review (Reflection):Students are provided with the opportunity to share their methods/discoveries, to present and explain.Teachers draw together what has been learned, reflect on what is important and summarise key facts.Teachers discuss next steps with students and make links to other work.

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The Basic Structure of a Maths Session

1. Warm Ups Concentrate on mental strategies. Provide opportunities for Working Mathematically. Review and practise previously taught skills and concepts. Mental maths could include number facts, number laws

and conventions. Games/activities designed to develop/practice WM skills,

use dice and counters. Use whole class oral counting activities, multiple/skip

counting, counting forward and backward from a given number, use of the open number line.

2. Main Activity

Modelling

Guided Practice

Independent Practice

New concepts/skills are presented to the whole class. What is to be learned, how it is to be learned, and what

students will be able to do is articulated. Skills/concepts/strategies are broken down from global

steps into sub-steps.

Students are guided through examples, feedback is given in response to student inputs.

The process involved is talked about, student to student, teacher to student, student to teacher.

New skills are practised with minimum teacher intervention or direction.

Students are used to teach students. Opportunities are provided for students to apply

skills/concepts explicitly in a variety of contexts. Provide opportunities for students to demonstrate

understandings.3. Lesson Review Students are provided with the opportunity to share their

methods/discoveries, to present and explain. Teachers draw together what has been learned, reflect on

what is important and summarise key facts. Teachers discuss next steps and make links to other work.

Overriding Principles

Acquisition A need for 80% - 100% accuracy

Fluency A need to get better, faster

Maintenance Be able to remember the skill over time

Generalisation Be able to use the skill in other contexts

Session ReviewIt may take students a number of experiences before they grasp a new skill or concept. A new skill needs to be repeated in a variety of contexts before mastery may be achieved.

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Outcome unit of work coversheet

STAGE 1Early Stage One Stage One Stage Two

MES1.5 Sequences events and uses everyday language to describe the duration of activities

MS1.5 Compares the duration of events using informal methods and reads clocks on the half-hour

MS2.5 Reads and records time in one-minute intervals and makes comparisons between time units

Working Mathematically OutcomesWMS 1.1 (Questioning) Asks questions that can be explored using mathematics in relation to Stage 1 content WMS 1.2 (Applying Strategies) Uses objects, diagrams, imagery and technology to explore mathematical problemsWMS 1.3 (Communicating) Describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbolsWMS 1.4 (Reasoning) Supports conclusions by explaining or demonstrating how answers were obtainedWMS 1.5 (Reflecting) Links mathematical ideas and makes connections with generalizations about, existing knowledge and understanding in relation to Stage 1 content

1 2 3 4 5 6X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

estimating and measuring the duration of an event using a repeated informal unit e.g. the number of times you can clap your hands while the teacher writes your name

comparing and ordering the duration of events measured using a repeated informal unit

naming and ordering the months of the year recalling the number of days that there are in each month ordering the seasons and naming the months for each season identifying a day and date using a conventional calendar using the terms ‘hour’, ‘minute’ and ‘second’ using the terms ‘o’clock’ and ‘half-past’ reading and recording hour and half-hour time on digital and analog clocks

X

XX

X

XX

XXX

Registration

Literacy Strategies Overview:Writing an explanation

Glossary

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Outcome Syllabus unit reference

Continuum of outcomes for teacher information

Working mathematically outcomes Stage 1Mapping grid allows teacher to see outcomes and knowledge and skills addressed in the lesson

Literacy support strategies

Glossary of terms that students may find difficult and are part of the required language


Outcome lesson

St 1 MS1.1 Estimates, measures, compares and records lengths and distances using informal units, metres and centimetres

Lesson: 2

Lesson focus: Curved and linear lengths can be measured

Start Up/ Problem: This string is the measure of the distance around an object in this room. What is the object?

Lesson Timeframe: 45 minutes

using informal units to measure lengths or distances, placing the units end-to-end without gaps or overlaps

counting informal units to measure lengths or distances, and describing the part left over comparing and ordering two or more lengths or distances using informal units estimating and measuring linear dimensions and curves using informal units recording lengths or distances by referring to the number and type of unit used describing why the length remains constant when units are rearranged

Materials: string, pop sticks, unifix cubes, match sticks

Activity Questions / Comments / DiscussionStep 1: (Whole class discussion) [5 –10 min]Discuss the measurement of length and the terminology used.Discuss how to measure head size (and why we would need to, eg hats).Discuss how to measure straight objects in the room eg desks, blackboards, cupboards (and why we would need to measure them).Students may suggest and demonstrate some alternative methods which could be discussed by the class.Teacher emphasises the skills of placing and

What are we measuring when we use the words long, short, longer than, shorter than, the same

length, shorter than?How could we measure the length around your head? (wrap a piece of string around and then find out how many unifix cubes long the string is)How could we measure the length of a desk or blackboard? (place string from one end of object to other, then find out how many unifix cubes long the string is)

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Outcome

What the teacher is trying to achieve in the lesson Some lessons may start with a problem

Knowledge and skills focused in the lesson are in italics and underlined

Materials needed for the lesson This part of the lesson indicates the types of questions the teacher should be asking the student. It provides directions for the teacher in the lesson. Where the working mathematically outcomes are utilised WM with the outcome number is written. Eg Working Mathematically 1.5 is WM 1.5

This part of the lesson indicates the time allocated for the step and the teaching activity for students. It also specifies when the students are to be in whole group, pairs or groups.


counting the measuring units when laying the unifix cubes along side the string.

Should we overlap the string where the two ends meet? Why/why not? [WMS1.2]

How can we record the head measurements?How can we record the length of the objects (eg blackboards, desks)? [WMS1.5]

Step 2: (Small group) [20-25 min]Explain that the task is to work with a partner to:

measure the distance around their heads measure the length of the blackboard

using a string and unifix cubes, popsticks etcStudents assist each other to:

measure around heads measure the length of the blackboard

Give students a copy of worksheet 2Students choose, align, count and record the number of units used to measure.

This may be an opportunity for individual assessment to check that students have:

chosen one kind of unit aligned and counted units correctly

[WMS1.2]

Step 3: ( Whole class discussion / reflection) [10 min]Report back to class

Which units were good to use and why? Can we compare head sizes if Andrew used blocks for units and John used matchsticks? [WMS1.3]

Key assessment points:1. See assessment worksheet

Application problemColour the balloon with the longest string.

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Specifies if any assessment within the lesson is taking placing

Some lessons have specific application problems. These problems may be taken from the Basic Skills Test and indicate the type pf skills the student should be able demonstrate.

The teacher should ensure that the students examine the types of strategies used by other students. It is important that the teacher summarise the key facts.


Monitoring student progress: How do I know when my students get there?

Monitoring involves systematic observation of students in order to observe the indicators identified that show achievement of syllabus outcomes.

The section in the document on assessment provides teachers with strategies, guidelines and examples for monitoring student progress.

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Assessment

While paper and pencil tests will continue to be an important method of assessment, teachers need to use a variety of assessment strategies. In mathematics, as in other curriculum areas, students learn from each other. Through purposefully talking over ideas together, students develop their understanding of mathematical concepts and enhance their enjoyment of mathematics. Teachers need to observe, listen to and collect the products of these learning experiences. Using a variety of assessment strategies will help to reduce students’ anxiety . (Mathematics K – 6, 1989 p 18)

Assessment is a critical part of the teaching learning cycle. It is through assessment that we know what it is that a student knows and can do. This is essential before we teach so that the lesson design can focus on progressing the student. It is useful to incorporate informal assessment opportunities during the lesson to observe student understanding. At the end of teaching a unit of work there needs to be an opportunity for a student to show what it is that s/he can now do.

In the following pages key questions are offered to help focus on opportunities to listen to students talking about their mathematical understanding and assessment ideas are provided to produce a work sample related to the concept addressed in the unit of work.

Assessment in NSW Department of Education and Training schools should be focused around student achievement of the learning outcomes.

An outcomes–approach acknowledges that students, regardless of their class or grade, can be working towards syllabus outcomes anywhere along the learning continuum.

An outcomes-approach to assessment will provide information about student achievement to enable reporting against a standards framework.

(School Assessment and Reporting Directorate (1997). Principles for assessment and reporting in NSW government schools.)

The NSW Department of Education has developed a variety of assessment tasks to assist teachers in determining the skills and strategies that students are using. The Starting with Assessment Materials and the Count Me In Too – Schedule of Early

Number Assessment (SENA) provide teachers with a one-one interview with students.

School Assessment and Reporting Directorate (1997). Principles for assessment and reporting in NSW government schools. Training and Developing Directorate (2000) Quality Teaching and Learning Materials

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Principles of effective and informative assessment and reporting

The following table lists attributes and focus questions as specified in the School Assessment and Reporting Directorate (1997), Principles for assessment and reporting in NSW government schools. The focus question provide teachers with questions to examine their own and school assessment practices and whether the principles are being met.

Attribute Focus question has clear direct links with outcomes

Do our assessment strategies directly link to and reflect syllabus outcomes?

is integral to teaching and learning

Are our assessment strategies derived from well-structured teaching and learning activities?

is valid Are our assessment strategies measuring the outcomes we intend to measure?

is fair Are we providing equal opportunities for success regardless of students’ age, gender, physical or other disability, culture, background, language, socio-economic status or geographic location?

is time efficient and manageable

How can we make assessment more time efficient and manageable?

is balanced comprehensive and varied

Do our assessment strategies give students multiple opportunities, in varying contexts, to demonstrate what they know, understand and can do in relation to the syllabus?

engages the learner Do our assessment strategies allow students to actively participate in the negotiation of learning tasks and actively monitor and reflect upon their achievements and progress?

values teacher judgement Are teachers confident to make judgements on the weight of assessment evidence and well-defined standards, about student progress towards achievement of outcomes?

recognises individual achievement and progress

Are we providing students with a wide range of tasks to ensure all outcomes and learning styles are catered for?

Examples of good classroom assessment strategies

Teachers need to select strategies appropriate to the outcomes they are teaching. Examples of the types of assessments that can be used are listed below.

Portfolio Three way assessment and reporting Performance assessment Observation sheets Journals Peer and self assessment

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Journals Teacher made tests

The following table indicates how the assessment tasks used in the exemplary programming units have been written and designed to meet the principles of effective and informative assessment and reporting.

Exemplary Stage 1 Mathematics Program assessment tasks

Attribute Assessment items in the Exemplary Stage 1 Mathematics Program

has clear direct links with outcomes

are linked with the outcomes

is integral to teaching and learning

all tasks are also teaching and learning activities

is valid measure the specific outcomes of that are being taught

is fair provides opportunities for students regardless of age, gender, physical or other disability, culture, background, language, socio-economic status or geographic location.

is time efficient and manageable

are incorporated in the normal lesson structure as teaching and learning activities

is balanced comprehensive and varied

provide a wide variety of tasks, from written, modelling, observation, etc

engages the learner allow the student to monitor and reflect upon their achievements and progress.

values teacher judgement help the teacher determine if the student is achieving the outcome

recognises individual achievement and progress

cater for the differing learning styles of students and ensure the outcomes are effectively assessed

A copy of the outcomes assessment record has been included after the assessment task.

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Example of Assessment Task in the exemplary programming units

Student Name: Date

St 1 DS1.1: Gathers and organizes data, displays data using columns and picture graphs, and interprets the results.

Lesson: 1

Knowledge and SkillsThe student can: Display data using concrete materials and pictorial representations Uses objects or pictures as symbols to represent data using one-

to-one correspondence Displays data using column graphs and picture graphs Interprets information presented in picture graphs or column

graphs

Record

St 1 M1.2a: Estimates, compares, orders and measures the length of objects and the distances between objects using informal units.

Lesson: 2

M1.2a IndicatorsThe student for example:

Compares and orders the length of objects by direct or indirect comparison

Compares and orders distances between objects Measures curves with informal units Estimates how many popsticks will fit along the teacher’s desk Uses popsticks to measure the perimeter of a large shape

Record

Students, in groups, collect data and then represent their data in a visual way. Students construct a sentence to explain their visual explanation.Students were asked to throw three beanbags from a single starting point. They were asked to

check the distances using a piece of string and to order them from the shortest throw to the

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longest throw. The students were then asked to record the activity and to discuss what they did and their results.

Word Boxlongest shortest distance length

throw beanbag string

Mathematics Outcomes Record

Name of Student:Teacher:Stage: 1 Grade: Date:

Key to reporting grid Understanding of outcomePT 1 BeginningPT 2 DevelopingPT 3 Consolidating

Outcome Progress towards reaching outcome

PT 1 PT 2 PT 3 OutcomeAchieved

Working BeyondStage

WM1.1 QuestioningWM1.2 Problem Solving

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Focus knowledge and skills indicator targeted in this assessment. Student may demonstrate other knowledge and skills indicators

Directions for the task. Student may not understand directions and teacher will have to explain to the class. Students are usually required to record in sentences.

Word box provides students with words used to make sentences.

Teacher may record student competency here


WM1.3 CommunicatingWM1.4 VerifyingWM1.5 ReflectingWM1.6 Using TechnologyS1.1 Representing 3D spaceS1.2 Representing 2D spaceS1.3 Spatial PatternsS1.4 PositionS1.5 Data RepresentationM1.1a Measurement attributes, units and toolsM1.1b Measurement attributes, units and toolsM1.2a LengthM1.2b LengthM1.3 AreaM1.4 Capacity and VolumeM1.5 MassM1.6 TemperatureM1.7a TimeM1.7b TimeN1.1 Whole NumbersN1.2 FractionsN1.3a Number FactsN1.3b Number FactsN1.4a Number OperationsN1.4b Number OperationsN1.5 Applying Number

Teacher Comment

Word Boxone two three four five more most less least

Using Literacy Strategies in Mathematics Lessons

A well-recognised teaching strategy is to begin a mathematics lesson with a contextual word problem. This requires students to read and comprehend the problem, often leading teachers to make the comment “I know they could do the maths if only they could read the problem”. It is quite appropriate for a teacher to allocate time for students to practise their reading and comprehension skills within a mathematics lesson. There are many literacy resources in

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existence to assist teachers improve students’ reading and comprehension skills. Many detailed descriptions of these are found in the DET State Literacy Book Programming and Strategies Handbook.

Examples of Contextual Word Problems with Suggested Reading Strategies

Problem: I had one of each of the coins in our currency on my table. I sorted them into two groups. What might the groups have been?

Stimulus: Problem Poster containing the problem in large print and pictures of several coins.

Suggested Reading Strategy: Think-aloud Reading (Whole class). This strategy has the teacher verbally modelling the thinking processes of comprehension (Making Predictions, Decoding, Describing, Making Analogies, Verbalising, and Monitoring Understanding.)Making Predictions : ”I think from the pictures of coins and this word coins this problem is about money.”Decoding: “How do I say this word?” Curr-en-cy, currency.Describing: “ I have a picture of some coins in my mind. Some are quite small. One is very big.”Making Analogies: I sorted them into two groups. “This reminds me of when we sorted the red and blue beads into two groups.”Verbalising: “Now, it might be good if we can get some coins to help with this problem.”Monitoring Understanding: “I wonder if I can work out the meaning of currency from the words near it?”Students can now move into groups of four, each group having a worksheet (A4 version of the poster), where students work cooperatively, again reading the problem and attempting solutions.

Problem: There are five vehicles in the car park. How many wheels might there be?Stimulus: A problem card strip for each group (pair) of students. Each group (pair) should have a competent reader acting as a tutor who could be a class mate, an older student, a mother, a STLD, etc).Suggested Reading Strategy: Neurological Impress Method: NIM (Paired reading). This strategy has the following purposes: to develop reading fluency, to model effective reading, and to build confidence. The tutor and a student read aloud together from the shared copy of the word problem.The tutor explains the process: We are going to read this problem out aloud together. You don’t have to worry about knowing all the words because I’ll be reading with you. You just say what I say. Keep your eyes on the words as my finger moves across the page and read aloud WITH me, not after me.The tutor must synchronise his/her voice and finger exactly, moving SMOOTHLY across the line of print and quickly from the end of one line to the beginning of the next. The text should be read with enjoyment and a discussion should take place at the end about what has been read.The tutor is NOT to correct errors or give negative comments. The reading experience must be a totally positive experience.Suggested Vocabulary Strategy: Word Meaning Checklist The purpose of this strategy is to help students become aware of when they do and do not understand the meaning of words.Stimulus: A half A4 sheet containing a prepared Word Meaning Checklist

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WORDS I know it well.I use it.

I know it a bit.

I’ve seen it or heard of it but don’t know it.

I’ve never heard of it.

five

vehicles

car park

many

wheels

might

.The teacher explains how to rate the words by modelling an example, carefully explaining the column headings using the bold words as key words. Ask the students to rate the words by ticking in the appropriate column. Use group discussion, synonyms and diagrams to assist students who place ticks in the last two columns.The text should then be read.

Concept of Definition

Purposeo To help students to develop and refine their knowledge of word meanings

DescriptionA word map is used to visually display different categories of relationships in a definition.

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To make a work map Selected word concept (1) The class to which the word concept belongs (What is it?) (2) The properties that distinguish it from other members of its class (What is it like?) (3) Examples or pictures of the concept (4) Similar examples of the concept

PreparationSelect a mathematical word from a current unit of work to use for demonstrating the construction of a word map.Complete the word map and use it to prepare a reconstruction activity, eg. a jig-saw or a cut and paste.

MaterialsOHT and blank copies of the word map.A reconstruction activity using a completed word map.

Implementation1. Explain the purpose of the word map.2. Model the process of constructing a word map. Provide explicit step by step instruction

using ‘think aloud’ and questioning.3. Use the completed example and materials provided for students to reconstruct the word

map. This could be completed as a whole class or small group activity with the class teacher guiding the process.

4. Select another familiar concept word related to the current unit of work and repeat the steps 1 to 3.

Example: Construct a word map based on the word Square.

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Word Map

DrawingDrawing Drawing

Description

4 straight sides

4 equal sides

Description

Flat

Description

4 corners

What is it?

2D Shape

Description:A square has 4 straight sides and 4 equal sides. It is a 2D shape, which means it is flat. It has 4 corners. A square is a bit like a rectangle.

Similar Example

A rectangle is like a square that has been stretched


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Word Map Map

DrawingDrawing Drawing

Description

Description

Description

What is it?

Description:

Similar Example


Directed Reading Thinking Activity (D.R.T.A.)

Purposeo to develop critical reading skills and the ability to predicto to support the incidental learning of vocabulary.

DescriptionD.R.T.A. is a silent reading activity during which participants stop and hypothesise about possible information or events ahead. Different views are discussed, using the text already read as supporting evidence.

PreparationStudents work in groups of three to six. Divide the problem to be read into suitable sections for evaluation. Dependent readers may need to have text read in groups or by a partner.

MaterialsA contextual word problem containing a title and multiple sentences appropriate to the topic being studied.Eg. Adam’s Water Bottle

Adam’s water bottle holds two litres of water.

Colour the number of ½ litre cups Adam could fill using all the water in his water bottle.

Implementation1. The groups sit in a circle to facilitate discussion.

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2. The students start by reading the title and predict what the problem will be about. If there are any diagrams or illustrations use these to make more predictions.

3. All students read at the same time to the end of the first sentence (evaluation point).4. Students set purposes for reading (for example, to find answers to focus questions).5. The students predict what the next sentence will be about, and consider the accuracy of

earlier predictions.

The Teacher’s role during D.R.T.A. ACTIVATE

What do you think? What will happen? AGITATE

Why do you think so? REQUIRE EVIDENCE

Prove it! Read the part that supports you.

The students role during the D.R.T.A PREDICT

Set purposes READ

Process ideas silentlyReread to justify predictionsRead orally, to substantiate beliefs or proposals

QUESTIONOthers in the group.

SUBSTANTIATEfrom evidence in the problem or your own experience.

Reading Graphs

Purpose To focus on graphs and interpret the content

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To practise ‘reading’ graphs and linking with associated content To link talking and listening vocabulary with reading and mathematics vocabulary

DescriptionThere is a very simple technique during which learners look at the non-print part of a text and talk about it and record key words on cards. Cards form a databank.

This strategy is used when students know little about the topic to be studied.

This activity is suitable for small group work.

PreparationSelect a suitable graph for reading and interpretation.

This graph shows how much rain fell during December, January and February.

MONTHS

In which month did the most rain fall ?o Decembero Januaryo February

Material1. Graph big enough to allow the group to see the text and information2. Index cards or similar, marking pens

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Implementation1. Discuss the title and topic of the graph with the group.2. Appoint a student as recorder or have students take turns [or the teacher may be

recorder].3. Draw the group’s attention to the names of the axes and discuss them with the students.

It may be useful to read these names to the students.4. Ask the students to ‘read the graph’ by naming items or ideas it suggests.5. Teacher may need to guide discussion to bring out particular vocabulary which they

know is associated with ‘reading’ graphs, in particular the language of comparison.6. Record any vocabulary that emerges. When the graph has been treated have the

students match the recorded words to the graph where they may be used.7. Display words during the duration of the concept being taught.

Making Predictions Using Graphs

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Purpose

To motivate students, activate content knowledge, increase anticipation and highlight important concepts. This technique introduces new technical vocabulary and allows discussion of new concepts.

DescriptionPredicting requires the students to make a judgment or best guess about what a graph will contain. This is a process of preparing the mind-set for what is to come.

MaterialCareful choice of graph at appropriate level.

Implementation1. Display the title of the graph, either on OHT or by preparing a copy large enough for the

whole group to see. Reveal the heading only.2. Students discuss, in pairs, groups or as a class, what the graph may be about. All

suggestions are acceptable. They share their reasons for their prediction, in answer to questions like ‘What made you think that?’ This helps students to identify and interpret a wider range of clues.

3. Students predict information that might occur on the graph.4. Display the graph, students read to verify predictions.5. After reading and interpreting the graph, students write down what they can remember

and check with their partner.6. Students discuss what they remembered and why they remembered that part.

Display first NICOLE’S VEGETABLES

Discuss/Predict

Display second NICOLE’S VEGETABLESDiscuss/Predict

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Display Third NICOLE’S VEGETABLESDiscuss/Predict

Display fourth NICOLE’S VEGETABLESDiscuss/Predict

Display lastDiscuss

The total number of vegetables grown by Nicole was:o 18o 24o 27o 28

Barrier Games

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Purpose To develop skills in oral description.

DescriptionBarrier games involve one player giving instructions while a second player receives and acts upon them. The two players are arranged opposite each other with a barrier between them. One player gives instructions while the other asks questions to clarify them. After receiving instructions and clarifying them in this way, the barrier is removed and a comparison of the material is made.

PreparationSelect an appropriate activity where a process can be articulated.

Example: 1A barrier is placed between each pair of students.Give each pair of students eight multilink cubes, two cubes of four different colours.Student one makes a construction using all eight blocks. This student then instructs student two to copy the construction. Student two asks questions to clarify the process.The barrier is then removed and the two constructions are compared.

Related OutcomeS1.1 Describes 3D objects using everyday language, models and sorts them, and recognises them in drawings and pictures.

Example: 2A barrier is placed between each pair of students.Give each pair of students a map. One map has a route marked on it.

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R

B BYY

R

W

W

BARRIER

R W

R Y

B

B

WY


The student with the route marked instructs the other student to follow the same route. The second student asks questions to clarify the process.The barrier is then removed and the two routes are compared.Variation: 1. No route is marked on the first map. The first student decides upon a route, draws it onto his/her map, and then gives instructions to the second student.2. Places are marked on the map. The first student is instructed to plot a route between two places, and then gives instructions to the second student.

Related OutcomeS1.4 Represents the position of objects using models and sketches, and uses everyday language to describe their position.

Reciprocal Teaching

Purpose

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To improve students’ comprehension of text through practice in previewing, predicting, self monitoring of understanding, questioning and summarising. It is particularly suitable for factual texts.

DescriptionReciprocal teaching focuses on before, during and after reading. It is a set of procedures to assist students to learn strategies, to know when to use them and to recognise that they are using them. They are most appropriate for students who can decode text adequately but who have difficulty understanding what it means. Four strategies are embedded in reciprocal teaching.

Predicting Clarifying Questioning Summarising

Reciprocal teaching is suitable for small groups, not the whole class. This procedure requires a training period in which the teacher models all roles, then gradually hands over the leader’s role as members take turns.The use of group roles helps this strategy: they are teacher, recorder, encourager, timekeeper. Students will need preparation for working in groups.

PreparationThe students need to be taught the steps in this technique so that they can eventually take turns being the “teacher” of the group, leading the students through the strategy as it applies to text in the KLAs.If it is to work well, students need to use it regularly during a unit of work. Three half hour lessons using the technique are probably needed each week.

MaterialsAppropriate text. If the text is too hard for some students it should be read aloud.A response sheet for the group (or individuals in the group) to complete.

Implementation1. predicting Students use their background knowledge along with the title and pictures to

guess and discuss what the text might be about. The teacher directs students to clues, eg “What does the title suggest?”

2. reading Students read the text silently, or aloud in pairs or as a group.3. discussing Were our predictions correct? What else happened?4. clarifying All students are encouraged to note words to be clarified as they read. The

“teacher” asks can anyone help.5. questioning Students ask three types of questions:

“right there” questions have answers right there in the text, probably in the same sentence as the words used to form the question.

“think and search” questions are inferential. The answers are more difficult to find but the evidence is in the text.

“on my own” questions can be answered by the reader only. Whilst the answer isn’t in the text, questions relate to it and answers should be justified.

Students are taught to identify the question types and to formulate all three types of questions. What number should be added to 7? Who can tell me what type of question this is and give me a reasonable answer?

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6. summarising The “teacher” summarises what has been read so far. Only the main points are stated. Graphic outlines can assist students in summarising.

7. predicting The cycle starts again until the text has been completed.

ExampleA train has some carriages. Each carriage has some people in it. Draw the train so that the order of the carriages from the front is different from the number of people in it.

The “teacher” introduces the text with a brief discussion to activate students’ prior knowledge.

All students read the text, alone, then aloud in the group. The “teacher” summarises, questions, clarifies & predicts. The students work through the problem to find a solution. Solutions are shared with the group.

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Reciprocal Teaching


Name: Date:

Predict Clarify

Questions

Summary

Here, Hidden, Head (3H)

Purpose To teach learners where the answers to questions can be found, using the mnemonic

cue 3H for:1. HERE the answer is explicit in the text. It is here in one sentence in the text.2. HIDDEN the answer is implicit in the text. It is found by joining together

information from two or more places in the text, or from information from the text and what the student already knows.

3. In my HEAD the answer is in the student’s background knowledge: what they already know.

Description 32


Students are taught this instructional strategy for answering questions. They apply the strategy to both asking and answering questions about text. The strategy can be used in individual and small group interventions as well as in classroom teaching.

MaterialsA selection of contextual word problems eg from past BST papers.

Implementation1. The teacher demonstrates the process, moving from the more basic level of decoding,

self-correcting and rereading to the comprehension level of question reading and answering.

2. The teacher directly teaches the first mnemonic cue (here), and uses think aloud strategies to teach reviewing, skimming and scanning techniques to find the answer.

3. The teacher supports the students in guided practice of the first mnemonic cue.4. The teacher supports the students in guided practice of the hidden mnemonic, and sets

some independent work on easy text in both the here and hidden strategies, and has the students frame their own here and hidden questions.

5. The teacher adds the in my head strategy in the same manner. The pace and degree of support will depend on the response of the students to learning the strategy.

6. Once taught, the 3H strategy is used by the students on a variety of word problems. The teacher at first reminds the students to use the strategy, but lessens the prompt as students begin to use it automatically.

Problem: A train has six carriages. Each carriage has some people in it. Draw the train so that the order of the carriages from the front is different from the number of people in it.

Once the 3H method is used regularly the teacher would: Read through the word problem, or get students to read it. Ask the students to identify the questions they would need to ask in order to find a

solution. eg “How many people could there be in the first carriage?” “How many carriages are there?” List the questions on the board.

Identify Here, Hidden or Head questions. When students have sufficient information, they begin to solve the problem.

Related OutcomeWM1.2: Answers mathematical questions using objects, pictures, imagery, actions or trial-and-error.

Fit It

Purpose To reinforce meaning and definition of vocabulary.

DescriptionA game based on the cloze technique. Students can develop their own games based on this model.

MaterialsTwo packs of cards; a sentence pack and a word pack.Each card in the sentence pack has a sentence with a word missing. A gap indicates the position of the missing word.

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The word pack has the missing words from the sentences.

Implementation1. The object of the game is to try to match a sentence and a word card and so accumulate

as many pairs as possible until there are no cards left.2. The winner is the player with the most pairs.3. If four people are playing, play in teams of two, thus allowing partners to confer and

decide together.4. The sentence cards are placed in a pile, face up. Word cards are spread out, face down.

Teams take turns to select the top sentence card and turn over one word card. 5. They read aloud the sentence card, inserting the word from the word card in the

appropriate place.6. If the sentence makes sense, they keep both cards and have another turn. If the

sentence doesn’t make sense, they place the sentence card on the bottom of the pile and turn the word card back over.

Related OutcomeN1.3(a) Represents addition and subtraction facts up to twenty using concrete materials and in symbolic form.

Fit It Sentence Cards (Game: 1)

7 plus 9 is 8 plus is 16

4 plus 7 is plus 7 is 15

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9 plus is 9 5 plus 9 is

___ plus 6 is 11

16 8

11 8


8 4 is 12 5 plus 5 is

10 plus is 15 3 plus 8 is

20 is 10 plus 14 is plus 7

2 plus 6 is

Fit It Word Cards

35

10

11

7

148

5


plus

5

10

Fit It Sentence Cards (Game: 2)

nine plus three equals

four plus equals fourteen

plus six is fourteen

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0

twelve ten

eight equals

six


nine plus eight seventeen

one plus equals eight

thirteen equals seven plus

Fit It Word Cards (Game: 2)

seven

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Neurological Impress Method (NIM)

Purposeso To develop fluencyo To model effective readingo To build confidenceo To connect the written symbol to the sound

DescriptionA tutor (peer or parent) or teacher and student read aloud together from one shared copy of the text.

PreparationSelection of appropriate students for the program and training of the tutor.

MaterialsThe text selected should be targeted to the individual child. For example, if a student is having no difficulty recognising the numerals 0-10 and 20-100, but confuses the teens, the following text could be used.

10 11 12 13 14 15 16 17 18 19 20

12 17 10 19 11 16 13 20 15 18 14Implementation

1. Sit next to your student.2. Explain the process which will take place like this: We are going to read these numbers

together. You don’t have to worry about knowing all the numbers because I’ll be reading with you. You just say what I say. Keep your eyes on the numbers as I point to them, and read aloud with me, not after me.

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3. Synchronise your voice and finger exactly, moving smoothly across the line of numbers. Use your finger above the line.

4. Read naturally. Find a comfortable speed.5. Stop at the end of each line and give a positive comment.6. DON’T CORRECT ERRORS and DON’T GIVE NEGATIVE COMMENTS. The program

must be a totally positive experience for the student.

Other Possible Useso Number words.o Multiplication tables.o Addition / subtraction facts.o Shape names.

Developing Sight Vocabulary: Match-to-Sample

Purposeo To increase the student’s sight vocabulary using the match-to-sample teaching strategy.

DescriptionMatch-to-sample is a teaching strategy that enables the teacher to control the presentation of activities in an easy to hard sequence to ensure success. When used for word recognition it enables the student to focus on the salient features of the word without reference to contextual clues. Daily practice and monitoring are necessary for progress.

The following is an easy to hard match-to-sample for teaching a single word.1. Meaning to meaning. Given a picture, find an identical picture.

2. Print-to-print matching. Given a printed word, find or cover the same word from a set of printed words.

3. Oral to meaning. Given a spoken word, select a picture from a set of pictures.

4. Meaning to oral. Given a picture, name it.

5. Oral to print. Given a spoken word, select the printed word.

6. Meaning to print. Given a picture, selected the printed word.

7. Print to meaning. Given a picture, select or find or frame the printed word.

8. Print to oral. Given a printed word, name it.

PreparationMake a square grid sheet by dividing a sheet of A4 paper into sections (no more than eight) with matching word cards.

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Implementationo Ask the student to match the word cards that are the same on the grid sheets by

covering them.o Tell the student to point to or to pick up the words as you say them.o Ask students to say the word on each card as you present it.

When a word is correct for three consecutive days, a new word can be substituted.

Developing Sight Vocabulary: Games for Word Recognition

PurposeTo increase the student’s automatic recognition of high frequency words, shapes, signs and symbols using games for daily practice.

DescriptionGames can be a fun way of providing daily practice for those students who have difficulty developing automatic recognition of many high frequency words, shapes, signs and symbols.

PreparationIdentify key words, shapes, signs and symbols and match to suitable games. (DENS Stage 1)

MaterialsGame boards, dice, counters, teddies, blocks, a laminator etc.

Types of GamesConcentrationBingoBoard gamesCard games

VariationsThese strategies can be revisited and used as new and more complex words are required by the students.

Other Word Recognition Strategieso Ensure that high frequency words, signs, shapes and symbols taught are repeated often

in context.o Display a data bank of high frequency words, signs, shapes and symbols in the

classroom for reference.

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o Have available a pack of high frequency words, signs, shapes and symbols with the sight word, sign, shape or symbol on one side, and a simple, easy to read sentence containing the word, sign, shape or symbol on the other.

o Cut up sentences to focus attention on individual words, signs, shapes or symbols.o Provide an individual folder for students that can be used to store a set of words, signs,

shapes and symbols for future practice at school and at home.

Look, Say, Cover, Write, Check – a strategy to support visual knowledge.

Purposeo To assist students to learn irregular words. It is not suitable for phonemically regular

words.

PreparationThe words that the student most needs to learn are the high frequency irregular or key words that he or she misspells. Students should not be required to learn words they already know how to spell. Select key words for a particular unit and give a pretest.

MaterialsPencil, workbook, paper or whiteboard. A prepared sheet, with four columns, requiring the student to repeat the process three times with each word.

Implementation

When looking at an outcome, think about the scope and complexity of the language demands for your students, especially those with weak literacy skills. While the correct spelling of these words is not vital, it is important for students to recognise these words and understand their meanings, especially the irregular words. It is also a strategy that can be used by parents at home to help their children. For example:

Outcome N 1.4(a) A student generates and describes number patterns using a variety of strategies.Relevant Syllabus Units N1-11, A1-3, S1-5, M1-3, D1-2Language: doesn’t belong, short, heavy, light, empty, enough, fewer, too many, fewest, nearly, fourth, seventh, eighth, ninth, equal, nought, goes, enough, two, four, among.

Say

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When saying the word, the student focuses on the parts of the word that are spelt the way it sounds.CoverBy covering the word the student is forced to rely on memory. Just copying words is not effective in helping students to remember them.WriteThe test: how much of the word is remembered correctly?CheckThe student compares his/her word with the original. Encourage the student to tick every correct letter.

Must, Should, Could: which vocabulary should we focus on in a topic?

Purposeo To assist the teacher to prioritise vocabulary where there are a number of new terms to

be learned.

Implementation1. List the words you think will cause difficulty for learners.2. Tick the words you have already taught, they only need revising.3. Categorise the remaining words as:

MUSTo Essential to learning the topic or concept.o Need to be systematically taught to enable learners to recognise and understand

them on sight.SHOULD

o Highly significant to understanding the topic or concept.o Students should know them.

COULDo Not essential for basic understanding of the topic or concept.o Teacher can still teach them but with less emphasis and review.o Decide how to teach the MUST and SHOULD words.

ExampleVocabulary Sheet: Outcome S 1.1 Describes 3D objects using everyday language; models and sorts them, and recognises them in drawings and pictures.Word Revise Must Should Could Examples of StrategiesSmooth √ QuestioningCurved √ Questioning, diagrammingRounded √ Questioning, matching

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Pointed √ Questioning, matching, diagrammingLonger √ Demonstration, questioningShorter √ Demonstration, questioningFlat √ Demonstration, questioningBalance √ Questioning, diagrammingRoll √ Demonstration, questioningSlide √ Questioning, diagrammingTwist √ Questioning, diagrammingTurn √ Questioning, diagrammingSquash √ Questioning, diagrammingFlatten √ Questioning, diagrammingHollow √ Questioning, matching, diagrammingSolid √ Questioning, matching, diagrammingFace √ Questioning, matching, diagrammingEdge √ Questioning, matching, diagrammingCorner √ Questioning, matching, diagrammingSquare √ Questioning, matching, diagrammingTriangle √ Questioning, matching, diagramming

Mental Computation

Calculating numerical problems mentally was regularly used in classes many years ago where the emphasis was on producing an answer quickly. These problems were either called mentals or mental arithmetic. There was no attempt made to analyse the method used. Today students are being encouraged to use mental computation which emphasises the mental processes used in working towards an answer. With mental computation students choose their preferred strategy and are then asked to verbally explain their thinking.Mental computation, within the teaching of mathematics, has been much undervalued, with written computation making up almost 100% of the teaching time of many teachers. This has resulted in some students attacking addition and subtraction problems using the trading method exclusively, even at inappropriate times. An extreme example of this is

1 15 - 7___________

Teachers are encouraged to promote the use of mental computation in their students by providing opportunities for students to orally explain their chosen strategy. Ideally, several strategies will emerge around the same task and each should be discussed in terms of ease and efficiency. Students, when faced with a problem, are then more able to make a choice of a strategy appropriate to a particular problem.

Subtraction involving zerosSubtracting 76 from 100 is quite a messy method using trading whereas a bridging to 10 mental strategy is much more efficient, i.e. jumping 4 to 80 and then incrementing by 10 to 90 and another 10 to 100, giving an answer of 24.This example involves two sub-skills; bridging to 10 and incrementing by 10.

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The bridging to 10 strategy involves students being exposed to many examples of the combinations of 10, sometimes referred to as Friends of 10. These being 8 & 2, 9 & 1, 6 & 4, etc. Friends of 10 can be found in DENS 1, p. 175. Other activities include using the student’s 10 fingers. Once instant recall of the combinations of 10 has been achieved move onto two digit numbers where a two-stage question can be posed and practised. eg “46. How many to the next decade number and what is the decade number?” (Answers: 4, 50). A slightly different mental strategy involves incrementing off the decade numbers first.Subtracting 76 from 100 using this strategy becomes: start with 76, then 86, 96 (twenty), bridging from 96 to 100, 4 (hence, twenty-four).

Doubles, Near Doubles and CompensationAnother mental computation strategy involves number-doubles and near-doubles. Having learnt the number fact 7 plus 7 is 14 leads onto 7 plus 8 is 15 and 7 plus 6 is 13.The use of compensation is a useful strategy with awkward numbers, particularly with near decade numbers of 47 plus 19. “I don’t like 19, but I like 20.” Now 47 plus 20 is 67. But, I need to compensate for changing the 19 to 20. Because I made the 19 larger by 1 and I was adding it to another number then the total must be larger by 1. Hence, the total of 67 must be larger by 1, giving an answer of 66.

Mental Computation and AssessmentTeachers may feel an assessment difficulty can arise with the use of mental computation as there is no written evidence showing the method used compared to students producing written algorithms. Assessment will need to be individual and care should be taken to both value the attempts made by the student and to allow sufficient wait time for the student to try to verbally explain the chosen strategy.When teachers are modelling particular mental strategies it is often useful to use either an empty number line or a partitioning diagram to illustrate the steps used in the strategy being modelled. As students become proficient in the use of these written methods they are then able to use them in the explanation of their mental method. It should be emphasised that these written forms are not seen as replacing the standard written algorithm but as a way of either the teacher or the student demonstrating the mental computation.

The Empty Number LineThis is a powerful tool to keep track of a series of mental steps when combining numbers.

48 + 25

One interesting aspect of this method is the point of entry into the addition. The standard written algorithm beginning is to add together the two units digits. This method begins with the tens and units digits of one of the numbers, then incorporates the skills of incrementing by ten and bridging to ten.A typical explanation by a student could be: “I started with the forty-eight and noticed I needed to add on twenty, so went fifty-eight, sixty-eight. Then I need to add on the five from the twenty-five. I took two out of the five to get to seventy and had three from the five left over which makes seventy-three”.The Empty Number Line should be used for the period of time that it takes a student to understand the steps involved in the method then it should be withdrawn, reverting to mental computation only.

44

48

1

58 68 70 73

10 10 2 3


Partitioning/Combining DiagramsA second useful written procedure for keeping track of mental steps is a diagram showing the various partitioning and combining of numbers within the calculation.

48 + 25

Like the Empty Number Line this diagram allows modelling of the mental thought processes used in the method. A typical explanation by a student might be: “I added the forty and twenty together to get sixty and the eight and the five to get thirteen. Then I added the ten from the thirteen to the sixty to get seventy then added the three from the thirteen to the seventy to get seventy-three. It is worth noting some students begin with adding the tens rather than the units whereas others will partition, then add units followed by the tens.

45

40 8 20 5

60 13

10 3

70

73

Partition

Combine

Partition

Combine

Combine

48 25


Teaching rural and Indigenous students

When teaching students in rural setting it is important not to bring preconception about their abilities or understandings to the classroom. Students in rural settings are no different from students in urban settings in their learning needs. They need access to the same learning outcomes as their urban counterparts. They have the same learning needs as their urban counterparts.

Factors affecting teaching and learning for students in rural settings

PedagogyTeachers may use teaching practices that do not sit with the learning styles and learning needs of their students. Many issues arise with the extensive use of textbooks as a focus by teachers as learning activities. Students become easily bored and those without sufficient literacy cannot engage with the learning activity. Few teachers give all students the identical reader. They will go to great lengths to match the reader with the student and yet teachers of mathematics often have all students do the same work from a mathematics text book.

Geographic IsolationIsolated students may have had quite different experiences to those of urban students eg: not having been to the beach or having travelled on an aeroplane, train etc. This may affect how students can effectively engage the curriculum as textbook focussed activities assume that all students have similar backgrounds.

Curriculum RelevanceWhile this is applicable for any student it becomes particularly relevant for students who can see no practical purpose or application. This can be of extreme relevance for Indigenous students where inappropriate curricula context can be a major factor for Indigenous student disengagement from learning.

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Education may not be seen as a valuable commodity by students who complete their School Certificate or Higher School Certificate as they may have limited employment opportunities. Many communities may not value education as students may end up working in the community where there is no need for further education.AttendancePreceding factors contribute to very low attendance by Indigenous students. This further impacts on the learning opportunities of students. As students construct new meanings based on what they already know and can do, missing whole blocks of work can have ongoing consequences.

Strategies to support rural and Indigenous students

The practices in this section which relate to rural and Indigenous students are equally applicable to urban students

All children have understandings that can be placed against the syllabus learning continuum. Rural and Indigenous students are placed against the same framework and teachers should have the same expectations.

The following statement taken from the Adelaide Declaration on National Goals for Schooling in the Twenty-First Century states that

“Aboriginal and Torres Strait Islander students [should] have equitable access to and opportunities in schooling so that their learning outcomes improve and over time, match those of other students.”

Learner-centred curriculumLearning should be directed for the teacher by the teaching and learning cycle. It should be engaging, relevant and meaningful. The learning in the classroom should emphasize the acknowledgment of the student’s social and cultural context.

Teachers need to adapt the syllabus in a manner to focus on the needs of the learner. They should be aware of the different learning styles of their students and recognise that one cap doesn’t fit all.

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The teaching and learning should focus on the achievement of syllabus learning outcomes by students. Students should be provided with learning activities that will allow them to acquire the necessary, skills, knowledge and understanding as outlined in the syllabus.

School, home and communityTeaching in a rural community is different to teaching in an urban community. It is likely that the teacher will be living in the community in which they will be teaching. There will be the likelihood that members of the community will closely monitor the actions of the teacher. It is essential that the teacher maintain a good relationship with the community in which they are living. Teachers should try and to make themselves aware of the local community culture and try to form links with the community. Knowing the students community well will assist the teacher in developing appropriate learning experiences. Being aware of the student’s home environment will also be beneficial.

Linguistic mattersLanguage is of critical importance in the teaching of mathematics. Teachers should be aware that the teaching of mathematics is not purely based on symbolic notation but is heavily reliant on literacy constructs.

Student engagement in mathematics should include discussion, problem solving, open-ended questions where students are encouraged to explain their strategies.

Strong literacy skills will enhance student performance in mathematics. Low performance on external testing measures such as the basic skills test (BST) can often be attributed to poor literacy skills preventing students accessing the questions. It is essential that teachers ensure that oral discussion, reading and writing are inbuilt into mathematics activities.Equity

Students need to be provided with necessary equipment to enable them to carry out their education. In particular, technology such as computers and calculators may be an issueshould be accessible. Another issue isT the high turnover of teaching staff. This may cause continuity problems or the loss of resources with teacher movement.

Teaching strategiesTeachers must utilise a variety of teaching strategies that cater for a variety of student learning styles.

Students should be provided with teaching activities that allow a gradual progression along a learning path.

There should be a wide variety of assessment and teaching tasks that cater for a wide variety range of ability.

Activities should integrate reading, writing, listening and speaking. Teaching should be explicit and utilise modelled, guided and independent components

within their lessons.

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Group work

Small groups help the students to: share and work collaboratively, develop a range of social skills, share and work cooperatively, use language to refine and consolidate mathematical understandings, develop mathematical understanding through active involvement, develop problem solving strategies. The opportunity exists for students to use their own language, to exchange ideas freely and to help one another understand in a meaningful way. Small group work assists teachers to: manage concrete materials effectively, teach students individually, have students work on different tasks or different aspects of a task, encourage students to develop useful work habits, encourage students to become self-reliant, encourage students to share and work cooperatively, evaluate student understanding.

Forming groups The planning of group activities should allow for varied and flexible groupings. Interest groups are useful when students are working on a project, ability groups are important to allow students to work at their own level, friendship groups are useful when students need to work harmoniously such as building a model, structured mixed ability groups are useful to encourage peer tutoring and at other times a random selection is useful.

Classroom climateTo establish a positive classroom climate for group work students need to experience success and satisfaction in programmed group activities. It is important to encourage and support

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students to foster the development of desirable group skills. Group work can also be used to encourage equal participation and reduce dominant behaviour.

Group sizesThe size of the group depends on the task. At times it is useful to have students working in

pairs. Think-pair-share is a valuable pre-assessment task where students begin by clarifying in his/her own mind, then share with a partner to clarify understanding and finally each pair combines with another and the foursome report on their negotiated understanding of the question/concept posed by the teacher. For more formal cooperative group work many

experienced educators advocate four as the optimum size. This optimises communication. If any two members of the group are talking the other two are not isolated.

Group RulesOnce your groups are formed there are three basic rules that should be in operation.

1. You are responsible for your own work and behaviour.

2. You must be willing to help any group member who asks.

3. You may only ask a question of the teacher if everyone in your group has the same question.

There are rules for the teacher too.1. Do listen.2. Do interact.3. Don’t ignore.4. Don’t interfere.

As caring and sensitive teachers we are used to responding to students directly and offering help whenever we can. With group work teachers need to step back and answer only if the

whole group the whole group agrees they need to ask. Success is not instantaneous. It takes practice, encouragement and discussion for students to learn to work together successfully.

IMPLEMENTING GROUPS

Teachers have found that working with small groups in the classroom enables them to: Vary the learning experiences to suit the needs of students' mathematical understanding Involve students more effectively in their own learning Divide the class into smaller units to allow the teacher to tailor instruction to individual

needs Facilitate interactional skills in students

Activities can be a mixture of instructional and independent; that is the teacher can work with one group while the others work independently. However the activities are designed and implemented, it is essential that the independent activities can be completed wholly unsupervised by the least skilled member of the group.

Group work has the added value of increasing social skills at the same time. Such skills can include:

Completion of a task independently Co-operation and collaboration

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Problem solving Sharing of resources

Designing a Manageable SituationActivities must be realistically chosen in terms of:

Preparation time Instructional time Supervision Noise Movement Resources Student independence

Possible problemsProblem Some SolutionsFormat of the activity given to independent groups is unfamiliar or too unstructured

Teach each format before assigning it as an independent activity

General disruption by groups who finish early and are unsure of what to do next

Have extension activities for groups who finish early

GROUPINGWhile the formation of the groups will be largely determined by the students' SENA results, it is important to also take into consideration factors which affect student progress while working in groups. These can include:

Student progress the lower performing students should not feel the failure of coping with instruction geared

to the middle achiever the higher performers are not frustrated by being held to the "middle pace" of instruction

Supervision If you wish to work closely with one group during a lesson, the other works will have to

work independently without disturbing you or Under the supervision of another adult (parent, community helper, more skilled student)

If you have a large number of students with low levels of achievement, you may have problems in maintaining independent working habits. In this case you may need to consider limiting the number of groups to the number of other adult helpers you can enlist.

Student participation The larger the group, the larger the pool for generating ideas The larger the group, the easier it is for the less extroverted/skilled student to avoid

participation Noise

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If the group work involves student interaction, you can expect some increased noise level. Your proximity to other classes will limit the amount of noise you can make and consequently the number of groups you can have.

If this is a problem, you could consider negotiating a swap to a room where the noise level will present less of a problem

Resources The familiarity of the students with the format and use of the resources will affect the

degree to which students can work independently and hence the number of workable groups

The numbers in the groups do not have to be the same but there will need to be enough of the resource for the largest group.

Preparation Preparation will have to be make for each group so the more groups you have, the more

preparation you will have If you intend spending intensive time with one group during a lesson, the other groups

will have to be working independently. Preparation for independent work will have to be thorough to avoid students disturbing you with questions.

In what circumstances will I regroup?Different re-grouping situations have positive and negative implications such as the following:

Changing membership of skill groups due to incorrect placement and or substantial change in skill level:

Facilitates instruction by reducing variability of skill level Is very motivating if the movement is to a group with higher skills Can be damaging to self-esteem if the movement is to a group with lower skills

Changing membership due to social relations distracting productive working: Is a logical move perceived by the teacher Runs the risk of student resentment and decreased motivation Runs the risk of students continuing the relationship from afar, thus disrupting the class

Changing membership to stimulate interest: Is good for when teacher and/or students are becoming complacent Change can be as good as a holiday

To help you evaluate progress you will need some type of product from the students, either individually or from the group as a whole. Feedback can include:

Demonstration to the group or class as a whole Tape recording of the group at work Written record of the task by the student Feedback from parent or other helper who you may work with

Such feedback can be used to: Give you direction on: Adjusting objectives for the group Adjusting the learning activities to facilitate progress Changing the composition of the group Give feedback to the student on his/her progress Provide feedback to others including parents

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SKILLS AND GROUP WORKWhat skills are needed?

Roles Leader Recorder Timekeeper Distributor of resources

IndependenceFinish task or go on to other workAsk appropriate questionsOrganise time and resourceIgnore distractionsFollow verbal and written instructions

Contribute to the group by:Contributing ideasTaking turnsCooperating with fellow group membersBe positive towards other group membersBe sensitive to other members' needs and feelingsBe able to give clear instructions to other group members

How are the skills taught?One approach to teaching the skills needed.

1. All students are taught skills/routines of working on individual tasks independently for a given period. For example, schedule a 20 minute period where the students:

Complete two tasks Locate and return resources for the tasks Place their work in a given spot when complete Locate and use extension material when the two tasks are complete

2. Teacher withdraws a group and trains them to do a task involving group interaction skills. The remainder of the students work on independent activities.

3. Other groups are formed and trained. While one group is working with the teacher, the other groups do independent individual tasks or group tasks which they have been previously taught.

In this approach the following procedures are important: No group work is attempted until all students can complete individual tasks

unsupervised. This tightens the organisational routines that will be used to an even greater extent in groupwork.

Group tasks that are selected initially should be simple

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The approach to establishing groups is a gradual one which relies on establishing firm foundations.

ADVANTAGES OF GROUPWORKFor the teacherClassroom climate

Promotes open communication Fosters cooperative attitudes Involves more student/student interest Makes teacher/pupil interaction more personal Provides an avenue for community involvement

Classroom organisation Develops student independence Gives students greater access to resources Spreads teacher time Widens participation, lessening need for teacher input

Levels of teachingProvides teaching and learning at varying levels:

Intellectual Social Interest Experience

For the studentAcademic success

Students are better able to work at their own pace Students have greater access to tutors Students' speaking skills are enhanced through greater opportunity for interaction

Attitudes to work Increased self esteem due to increased academic success Increased responsibility and independence Recognition of sources of knowledge other than teacher Enhances planning ability Students become active learners

Social skills Increases cooperation Increases participation Develops negotiation skills Sense of ownership of the work increases as students take responsibility in decision-

making

Emotional skills Understand others' needs Group engenders sense of belonging Smaller size of group increases confidence More opportunity for students to express themselves Increases self-awareness

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General learning Hear different interpretations Experience different ways of expressing ideas Develop questioning techniques Promotes more 'hands-on' experiences

Adapted from: Using Small Groups in the Classroom. Liverpool Region Inservice Committee [nd]

Language Considerations

Mathematics learning is promoted by appropriate use of language. Language, together with mathematical symbols and diagrams, plays an important part in the formulation and expression of mathematical ideas and serves as a bridge between concrete and abstract representations.

The acquisition of mathematical language develops through the use of the four interrelated processes – talking, listening, reading and writing. (Mathematics K – 6, 1989, p 26)

The language demands of mathematics are not all met within regular literacy lessons. Some explicit teaching needs to occur around the language of mathematics.

WORDSSome words are used only in a mathematics lesson and must be taught in this context. Eg. parallelogram, scalene. Other words have a different meaning in every day use to the meaning they have in a mathematics lesson. These need very careful instruction. Eg. Product is something that has been produced or the result of a multiplication. Volume may mean a book when the student is in the library, the level of sound when the student is singing and the size of a 3D object when in a measurement lesson.Yet other words have a different meaning even within different topics in mathematics. Eg square; meaning multiplying a number by itself or a regular quadrilateral. A third has two quite

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distinct meanings; gaining a third place in the race and the fraction . Teachers must be aware

of these and be careful not to confuse.

DENSITYMathematical word problems are referred to as being lexically dense. Whereas, when reading a novel the author reminds us in many ways about the setting by describing it with similes, metaphors and the like, a mathematics problem states the facts once and only once. What is also confusing, the order of the words can change the resulting problem. Skim reading may be an inappropriate technique for a mathematical problem. For example: The simple cloze passage Divide 6 ……. 3. If this became Divide 6 by 3. The answer would be 2.If, however it became Divide 6 into 3. The answer would be 1/2.A subtle change to this again makes Divide 6 into 3 equal groups. The answer reverts to 2 again.

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Documents

Programming in the teaching and learning cyclenumeracy4life.wikispaces.com/file/view/Exemplary+Stage+1... · Web viewIt is fundamental that all teaching is undertaken within the framework