How To Differentiate Mathematics Instruction Using Math Stations Fulton County School System Nelly Belinga-Hill Mathematics Teacher Math Department Chair

How To Differentiate Mathematics Instruction Using Math StationsFulton County School System

Nelly Belinga-Hill

Mathematics Teacher

Math Department Chair

Martin Luther King Jr High School

[email protected]

June 28th, 2011

Nelly Belinga-Hill

How To Differentiate Mathematics Instruction Using Math Stations


Agenda

1. Opening Activity: Choice Board (30 mins Thinking & 30 mins Sharing)

2. Morning Discussion: The Importance of Problem Solving in Mathematics (30 mins)

3. Connecting The Pieces: From Problem Solving to Station Teaching (30 mins)

Morning Break (10:30 – 10:40 am)

4. Differentiating Instruction: How Math Stations Help Differentiate Instruction (2h)

Lunch Break (12:40 – 1:40 pm)

5. Afternoon Session: Designing Your Own Differentiated Lesson(2h and 20 mins)

Essential Question

How can I use Math Stations to differentiate instruction in my classroom?

1. Opening ActivityChoice Board

Nelly Belinga-Hill


Problem solvingChoice board

Choose 3 activities You have 30 mins You must go through the center Think – Group (optional) - Share 10 mins 10 mins 10 mins

Draw Move

Around

Sing

Write

a Speech

Math Challenge Questions

Debate

Journal

Entry

Describe the Learning

environment

Role-Play

1. Opening Activity: Choice Board

Nelly Belinga-Hill


How many valentines?Solution To Math Challenge 1

There are five friends. For Valentine's Day, each friend gives each other friend a valentine. How many valentines are there altogether?

Next, extend your reasoning to a larger number, what if you had 28 friends?

Introduce yourself Share Some of Your Answers

1. Opening Activity: Choice BoardSource: http://www.learner.org/teacherslab/math/patterns/valentines/handshakes3_act.html?uid=0

Nelly Belinga-Hill


NCTM Standard 2 (1998)

Sets the purpose of patterns, functions, and algebra in mathematics education at all grade levels.

Mathematics instructional programs should include attention to patterns, functions, symbols, and models so that all students:

understand various types of patterns and functional relationships;

use symbolic forms to represent and analyze mathematical situations and structures;

use mathematical models and analyze change in both real and abstract contexts.

1. Opening Activity: Choice BoardSource: NCTM Principles and Standards (1998)

Nelly Belinga-Hill


Types of solutions

1. List Them All

2. Do Addition

3. Draw Points and Arrows

4. Make a Star

5. Make a Grid

6. Look for a Pattern

7. Use a formula

8. Just do it

Source: Annhenberg CPB/Math and Science Project


Nelly Belinga-Hill


Types of solutions List them all Do additionSuppose the names of the friends

are A, B, C, D, and E.

Let's list the valentines that each friend gives, starting with A's valentines.

A–B, A–C, A–D, A–EB–A, B–C, B–D, B–EC–A, C–B, C–D, C–ED–A, D–B, D–C, D–EE–A, E–B, E–C, E–D

That's 20 valentines.

Suppose the names of the friends are A, B, C, D, and E.

A gives 4 valentines

B gives 4 valentines

C gives 4 valentines

D gives 4 valentines

E gives 4 valentines

Add the numbers.

The total is 20 valentines.

1. Opening Activity: Choice BoardSource: Annhenberg CPB/Math and Science Project

Nelly Belinga-Hill


Types of solutions Draw points Make a starand arrows


Draw an arrow between each pair. Then count the arrows. There are 10 and each one represents 2 valentines. So that's 10 twice—a total of 20 valentines.

This solution is a lot like "Draw Points and Arrows," except we arrange the points differently.


Every arrow represents 2 valentines and there are 10 double-headed arrows. Again, that's 10 twice—a total of 20 valentines.


Nelly Belinga-Hill


Types of solutions Make a grid Suppose the names of the friends are A, B, C, D, and E. We make a grid of all

the friends. Each pink square is a valentine. The gray squares show that each person does not send a valentine to himself or herself.

Either count the pink squares (20), or notice that there are 5 x 5 = 25 squares in the whole grid, minus 5 gray squares. Thus 25 - 5 = 20 valentines.


Nelly Belinga-Hill


Types of solutions Look for a patternHere we look at even smaller numbers.

1. What if there were only one person? Then no valentines are given. Zero.

2. What if there were only two friends instead of five? Then there would be 2 valentines exchanged.

3. Three friends, there would be 6 exchanged.

4. Four friends, there would be 12.

5. What's the pattern? 0, 2, 6, 12,...?

Between the first and second numbers is a difference of 2. Between the second and third, a difference of 4. Between the third and fourth, a difference of 6. And so on. If the pattern were to continue, the next number would be a difference of 8—

and 20 valentines would have been exchanged.


Nelly Belinga-Hill


Types of solutions Use a formulaYou know that if there are n people, each will

send out (n - 1) valentines.

So the total number of valentines V is

V = n (n - 1)

Since n = 5 in this situation, V = 5 x 4 = 20


Nelly Belinga-Hill


Types of solutions Just do it

Get four friends.

Now there are five of you.

Give valentines to each other.

Then collect all the valentines and count them.

There are 20.

Source: Annhenberg CPB/Math and Science Project


Nelly Belinga-Hill


Checkpoint question:5-mins discussionsDiscuss – Summarize - Share2 mins 1 mins 2 mins

How do we build this type of reasoning across the grades (K – 12)?


Nelly Belinga-Hill


Across the grades

The youngest children begin simply by counting. They count by 1s, then by 2s, 5s, and 10s. These patterns give students a natural strategy to understand addition and multiplication. When considering a number pattern such as 2, 4, 6..., a young student will ask herself, By what number can I count (add) to get to the next number in the pattern and the next and the next?

As the student gets older, her knowledge of patterns advances from sums to products. When asked for the 50th number in the pattern, she will know to multiply 2 times 50.

High school students can start to understand functions, such as f(x) = 2x + 2, where x is the numerical sequence 0, 1, 2, 3,…. They begin with simple in-out machines and gradually adapt their understanding to the abstractions of algebra.

1. Opening Activity: Choice BoardSource: NCTM Principles and Standards (2000)

2. Morning DiscussionThe Importance of Problem Solving In Mathematics

Nelly Belinga-Hill


Discussion Question

Describe what is meant by “Problem Solving.” Why is this important? How is this different from the problem solving you see in most math books?

2. The Importance of Problem Solving

In Mathematics

Nelly Belinga-Hill


NCTM Standard (2000)Problem SolvingProblem solving means engaging in a task for which the solution

method is not known in advance.

In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings.

Solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking.


In Mathematics

Source: NCTM Principles and Standards (2000)

Nelly Belinga-Hill


Importance of Problem SolvingIn everyday life and in the workplace, being a good problem solver can lead

to great advantages. Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program.

By learning problem solving in mathematics, students should acquire ways of thinking habits of persistence and curiosity confidence in unfamiliar situations

Problem solving in mathematics should involve all the five content areas described in the NCTM Standard:

build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving.


In Mathematics

Source: NCTM Principles and Standards (2000)

Nelly Belinga-Hill


Problem Solving ArtifactsFound in Various Classrooms (Cont.)What to do if you get stuck

1. Read the problem again2. Look back at the lesson 3. Look back at the previous

work4. Look in the book5. Refer to the reference chart6. Ask your partner7. Ask the teacher

10 Steps to Success

1. Just keep trying2. Try to determine what’s

working3. Try to determine what’s not

working4. Try to find someone who has

done it5. Try and ask for help6. Try again tomorrow7. Try it a little differently8. Try one more time9. Try again10. Try


In Mathematics

Nelly Belinga-Hill


Problem Solving ArtifactsFound in Various Classrooms (Cont.)7 Steps to Solving Math Problems

1. Identify the ProblemWhat is the question asking?

2. Define the ProblemWhat will the answer look like?

3. Formulate a StrategyHow should I tackle this problem (VANG)?

4. Organize the InformationWhat information is given?

5. Allocate ResourcesWhere can I read more or learn more about this?

6. Monitor ProgressHow much time do I have?What are my steps?Do I need to use a different strategy?

7. Evaluate the ResultsDoes my answer make sense? Is this the best possible solution?

5 Steps to Solving Math Problems

1. Identify Problem- What is the problem asking you for?

2. Indentify knowns/unknowns- Organize given information

3. Translate known/unknowns into math symbols/language- Assign variables, subscripts and formulas as necessary

4. Solve for unknown

5. Check answer

4 Steps to Solving Math Problems

1. Look for clues 2. Establish a Game Plan 3. Solve the Problem

4. Recheck and Reflect.


In Mathematics

Nelly Belinga-Hill


Checkpoint Question

What type of Problem Solving Artifacts do you use in your classroom (or do you plan to modify and use)?


In Mathematics

3. Connecting the PiecesFrom Problem Solving to Station Teaching

Nelly Belinga-Hill


I spend

3 ½ hours

Online.

I listen to

music 2.5

hours a day.

I do 49% of the reading assigned.

I spend two hours on my cell phone.

I Face Book through most of my classes.

I read 3 books a Year.

3. From Problem Solving to Station Teaching

Nelly Belinga-Hill


I hear, and I forgetI see, and I rememberI do, and I understand.

Confucius

As teachers, we recognize that we are teaching a different generation with different needs.

It is therefore imperative to equip ourselves with tools that will help us address diverse learners, henceforth increase the engagement level.


Nelly Belinga-Hill


I Do and I Understand.What are Math Stations?

Math stations are areas in the classroom where students refine a skill or extend a particular math concept or concepts.

They may also be different places in the classroom where students work on tasks simultaneously, and whose activities are linked.


Nelly Belinga-Hill


Connecting the PiecesMath Stations - Problem Solving

Problem Solving

Students should acquire:

Ways of thinking Habits of persistence and curiosity Confidence in unfamiliar situations

Math Stations

Math stations are areas in the classroom where students refine a skill or extend a particular math concept or concepts.

They may also be different places in the classroom where students work on tasks simultaneously, and whose activities are linked.

Problem Solving

Math Stations


Source: Carol Ann Tomlinson “How to Differentiate Instruction in Mixed-Ability Classrooms.”

Nelly Belinga-Hill


Example of a Math Station LessonMath 1 Probability Lesson Video + Hands-On Experience


Nelly Belinga-Hill


4 Corner Picture Closing

4. How Math Stations Help Differentiate Instruction

….Math Stations Are Like….Because…..

Nelly Belinga-Hill


Types of Math Stations

Rotating Stations - rotate students through activities, or rotate activities through groups of students

Individualized Stations - students/groups only use the stations they need or to which they are assigned

Sequential Learning Stations - students must work through the activities in a particular order and proceed with mastery

Thematic Stations - all activities set up to support a specific unit of study

Enrichment Stations - stations that can be selected after assigned stations are completed


Nelly Belinga-Hill


• Whole class warm-up

• Review station assignments made based on pre-assessment

• Pull a group to the teacher’s station for a structured focus lesson.

• Other students work at their stations. You move around to monitor their progress when students at the teacher’s station are working in pairs or independently.

• Whole class closure activity.

• Whole class warm-up

• On grade level focus lesson for most of the class

• Above grade level students work on an anchor

• After focus lesson, students refine their understanding at a specific station or through an anchor activity

• Above grade level students receive their focus lesson at the teacher’s station.

• Whole class closure activity.


Nelly Belinga-Hill


Station Teaching Be PracticalDo

Begin where students are, not where you think they should be. Pre-assess.

Focus on the essentials so that struggling learners don’t drown in a pool of disjointed facts: Unpack the standard, explain the goal.

Articulate your expectations and spend time modeling the type of work found at each station. Work diligently to ensure that struggling, advanced, and in-between students think and work harder than they meant to; achieve more than they thought they could; and come to believe that learning involves effort, risk, and personal triumph.

Have a strong closing. Give students an opportunity to reflect on their problem solving skills: Math stations are not Math Games; they are learning centers.

Don’t

Do not ask Students to count off from 1 – 4 and form groups. Use your pre-assessment data.

Students do not move from station to station in a round-robin style. You determine which station and when!

Don’t just ask students to “Figure out the instructions.” Give clear instructions regarding material management, time management, direction of the movements, LOTS (Language of the Standard).

Do not sit at your desk and miss out on scaffolding opportunities. Build in time for you to circulate and use your questioning techniques.

Don’t work in isolation. Collaborate with your department to develop tasks for review, practice, and enrichment.


4. Differentiating instructionHow math stations help differentiate instruction

Nelly Belinga-Hill


Connecting the PiecesMath Stations - Problem Solving - Differentiated Instruction

Problem Solving

Math StationsDifferentiated Instruction


Nelly Belinga-Hill


GAPSS Instruction Standard 2.2 – All teachers make appropriate use of differentiation, including adjusting content, process, product, and learning environment based upon diagnosis of students’ readiness levels, learning styles, interests and personal goals.


Nelly Belinga-Hill


A class is not differentiated when assignments are the same for all learners and the adjustments consist of varying the level of difficulty of questions for certain students, grading some students harder than others, or letting students who finish early play games for enrichment.


Source: Carol Ann Tomlinson, 1995

Nelly Belinga-Hill



?

Source: Carol Ann Tomlinson, 1995

Nelly Belinga-Hill


Source: Calendra Brown, Fulton County Math Coach


Nelly Belinga-Hill


Differentiating by Learning ProfileChoice Board RevisitedVisual

Spatial Intelligence

Draw

Tactile

Bodily Kinesthetic

Move Around

Auditory

Musical

Sing

Linguistic

Write a SpeechLogical

Math Challenge Questions

Linguistic

Debate

Intrapersonal

Journal EntryNaturalist

Describe the Learning environment

Interpersonal

Role-Play

Group 1Group 2Group 3

Group 4

Nelly Belinga-Hill


What type of differentiation are we implementing?Send a Reporter in 5 mins to the other group.

Group 2

Develop Sensitivity For

Struggling Learners

1 Min Challenges

Group 2

Develop Sensitivity For

Struggling Learners

1 Min Challenges

Group 1

Breakout Activity

Handout #10a

Circumference Problem

Group 1

Breakout Activity

Handout #10a

Circumference Problem

AnchorScaffolding ProblemSolving: Focus on theProcess rather thanArithmetic

AnchorScaffolding ProblemSolving: Focus on theProcess rather thanArithmetic

Group 3Error AnalysisGroup 3Error Analysis

Group 4Vocabulary in MathGroup 4Vocabulary in Math


Source: Dr. Riccomini “RTI in Math”

Nelly Belinga-Hill


Differentiating by InterestQuestions to ask yourself

How will students use this topic in their worlds? How will the topic help students explain their own experiences? How will the topic contribute to or deepen students/ current

interests? How can the topic help students fulfill their aspirations? How can the topic help alleviate students’ fears and concerns? What will students gain if they learn this topic or lose if they do

not? What will happen if students use this new skill or knowledge well

and what will happen if they do not?


Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 47

Nelly Belinga-Hill


Differentiating by Readiness LevelDrain the Pool Learning Task

Question: If tasks at stations are the same for all students, are all students needs being met?


Lunch Break (1h)

5. Designing Your Own

Differentiated LessonAfternoon Session

Nelly Belinga-Hill


Source: Calendra Brown, Fulton County Math Coach

This MorningWe learned that…

5. Designing Your Own Differentiated Lesson

Nelly Belinga-Hill


Content Goal

Emphasize content knowledge. The main focus is on what students need to know or understand.

Example: Knowing the Meaning of Rate of Change within a real life context.

Key Verbs: “know, understand,…”

Source: Robyn R. Jackson “Never Work Harder Than Your Students” P. 59


Process Goal

Emphasize students’ learning or developing a skill. “Do it, and do know how and why!”

Example: Knowing how to compute the rate of change given 2 points, a linear or non-linear function.

Key Verbs: “Analyze, conduct, write…”

Designing Your Own Differentiated LessonUnpacking the Standard

Nelly Belinga-Hill


Competence

Choice

Creativity

Collaboration

Curiosity

I said so

Designing Your Own Differentiated LessonInclude the 5Cs


Source: Hanson, Silver, Strong “The 5 C’s of Interest and Engagement”

Nelly Belinga-Hill



Which Standard? How will you differentiate the lesson using station

teaching?

Nelly Belinga-Hill


Remember: Station teaching should produce “strategic learners”…

Able to analyze a problem and develop a plan. Able to organize multiple goals and switch flexibly from simple to more

complicated goals. Access their background knowledge and apply it to novel problem. Develop new organizational or procedural strategies as the assignment

becomes more complex. Use effective self-regulated strategies while completing a assignment. Attribute high grades to their hard work and good study habits. Review the goals and determine whether they have been met.

Source:

http://iris.peabody.vanderbilt.edu/ 5. Designing Your Own

Differentiated Lesson

Nelly Belinga-Hill


1. Please explain ________2. EQ: What are several ways that math stations can be used to differentiate

instruction in your math classroom?

Closing Activity


1

Very low

2

low

3

medium

4

high

My understanding of math stations

before the presentation

My understanding of math stations

after the presentation

Nelly Belinga-Hill


Make and Take…

To Create 1 Folder Game, you will need:

1 folder 4 pockets 1 folder game hand-out Scissors Glue sticks


Nelly Belinga-Hill

[email protected]

Math Stations Website:

Employees > Instruction > Math > Documents > Secondary Mathematics > Professional Development > Math Stations

Thank You Fulton County.