Improving Student

Understanding

Increasing student abilities in using Geometry and Spatial Sense

Language

Overall Goal

• The use of math language in the geometry and spatial sense strand

needs to be improved.

• This will be developed throughout the primary division to improve

scores in the grade 3 EQAO test

EQAO Results: A Cause for Concern

• the percentage of students performing at or above the provincial standard in

mathematics has decreased by three percentage points, from 70% to 67%

(EQAO Provincial Elementary School Report, 2013)

• the geometry and spatial sense was the least well performed strand in the

2013 EQAO test (EQAO Provincial Elementary School Report, 2013)

Even More Concerning:

• 19% of students met the math standard in grade 3 testing in 2010, and then

failed to meet standards in grade 6 testing in 2013

• This means that approximately 1/5 students (about 6 in every class) is

regressing mathematically, while only 5% of students who did not meet the

standard in grade 3 met the standard in grade 6

Solution: Begin Early

• 52% of students met the standard in both grade 3 and grade 6, which means

with early intervention, more students may be able to maintain a level of

success

• Increasing conceptual understanding of geometry concepts in early grades

through play can form a lasting understanding of knowledge needed for

EQAO

EQAO’s Suggestions

• “Engage students to communicate their understanding of lines of symmetry

by creating a responsive mathematics learning environment.”

• “Encourage students to describe their thinking using appropriate

mathematical language”

What we can do:

• As primary division teachers, we can work together to build a community of

math learners from kindergarten to grade 3

• By improving math language and creating a responsive math

environment in primary grades, students can have more success on EQAO

tests and in geometry

Developing Math Language

• Use a three-step approach to improve student math language

1) Play with math language, creating the responsive environment

2) Model confidence and competence of math and create a community of

learners creating comfort in the environment

3) Create a division-wide initiative to improve math language learning

extending the math learning environment

Play With Math Language

• Make jokes with math! Show students that math

can be fun

• Incorporate math language at all centres

• Make “cheat sheets” for yourself to keep around

the class if you do not remember math words.

This provides a good example of using resources

to students

Case Study: Theresa’s Kindergarten Class

• Theresa is the ECE in a kindergarten class that had great success in teaching her class geometry language with the FD-ELK team

• They did this using games, tactile experiences and repeating the language to students.

• At each center where the use of math language was targeted, educators left a “cheat sheet” out to remind themselves of the appropriate language

• When Theresa was not sure what the appropriate math language was, she consulted with a junior-intermediate math teacher

Perfection Centre

• At the math table, the game Perfection was

set out, and educators provided students

with the correct names for shapes, such as

“pentagon”, “parallelogram”, “decagon”,

“dodecagon”, “trapezoid”

• Students began to use the correct terms

and match them to the shapes

Block Centre

• Theresa made large 3-d figures out of cardboard for students to play with

• When students were engaged in playing with the blocks, educators gave

students the language to describe the blocks, such as “Oh, you want to use

the pyramid block for the roof?” “Ask him to pass you the rectangular

prism” “That’s the cube block”

• Within several weeks, students knew the names of all the 3-d figures, and

could describe the shapes of the faces, structure and other features

Book Centre

• Students were engaged in

literature that involved math

• Jon Scieszka’s Math Curse

video is featured

• While students may not

understand all the terms in

the book, they see math as

fun and enjoyable

Model Confidence and Competence with Math

• Never claim to not be good at math in front of your students- they will compare themselves to you!

• Highlight the fun and exciting applications of what you are learning

• Have strategies in place if you are uncomfortable with math: Theresa’s class had “cheat sheets” for the educators to refer to, she had colleagues she knew that she could ask math questions too

• If you don’t know the answer, find it with students, or show them how to find math answers with problem solving strategies or use an online resource

Create a Division-Wide Initiative

• As the primary division, could we:

• Create a math “word wall” in the primary hall way for all students?

• Have students create a math dictionary book that will travel with them throughout the primary grades

• Share resources, strategies and lesson plans to better enhance student understanding?

• Add a math “word wall” to the school webpage with definitions for parents to look at?

Lesson Planning

• The following slide shows a geometry and spatial sense question from the 2013

grade 3 EQAO math test and is the “model question” of our lesson plan

• This question relates to concrete materials, incorporates a picture, and expects

students to express a symbolic answer.

• This lesson plan provides a framework of how to address questions, that can be

varied for each primary grade level and class

• We need to teach students CONCRETLY→PICTORIALLY→SYMBOLICALY

Lesson Plan Template

Hook Body Consolidation

Introduce math language and

overall problem in a fun way

“Today, we’re going to look at

making different 2-d shapes with

pattern blocks. We’re making art

with pattern blocks”

Model math concept with

concrete materials, gradually

move to pictorial, then to

symbolic

“With your partners, have one

person make a design with

pattern blocks. Then the other

partner can try to cover it using

different blocks”

“You have had some time to try it

in pairs. Who can show us on the

SmartBoard?”

Review the key relationships

learnt, and demonstrate the

symbolic understanding

“Some pattern blocks cover each

other perfectly. It takes three

green triangles to cover one red

trapezoid. What other

relationships did you notice? Let’s

fill in this relationship chart and

hang it on our math word wall.

We can take a picture of the chart

to upload to our class webpage.”

Using Consistent Representations

• In the primary division, we will be implementing the blue “math table” and

yellow “manipulatives table” strategy shown in the following video

• If you teach math in a carpet circle, consider using a blue and yellow cloths

or trays that are portable and on the children’s level rather then raised tables

• The following video shows the use of the tables and moving from concrete

to symbolic representations in a British math class learning fractions

Consistent Representations

Planning and Implementation

• Classes are beginning their geometry and spatial sense units in the primary division:

at the end of the unit (1 month), we will meet again and discuss results

• Assessments: Goal is weekly assessment of use of math language. Each week, pick a

“marker question”, a question that requires a language-rich answer. Have students

submit their answers, and use the 4 level system to assess language use.

• While written answers are not the only way to assess student knowledge, it is the

only way used on EQAO. We want students to be comfortable showing their

knowledge in this way.

Levels

• Level I (incomplete) or B (blank): student does not provide answer, answer is not relevant to question

• Level 1: Answer does not include any appropriate math language

• Level 2: Answer includes some math language, but it is incorrect or irrelevant

• Level 3: Answer includes the math language that was taught, and it is applied correctly

• Level 4: Answer includes extensive math language that is clear and appropriately used

Goals

• When we meet again in one month:

1) Students will be able to demonstrate concretely, pictorially and symbolically

geometry and spatial sense concepts

2) Students will be better at expressing math ideas in writing with appropriate

language

3) Teachers will have worked to introduce math language and create a

responsive math environment

References

• EQAO: Student Assessments and Scoring Guides. (2013) Retrieved from

http://www.eqao.com/Educators/Elementary/036/BookletsandGuides.asp

x?Lang=E&gr=036&yr=11

• EQAO Provincial Elementary School Report. (2013) Retrieved from

http://www.eqao.com/ProvincialReport/Files/12/PDF/EQAO_Provincial

Report_Elementary2012.pdf

• Personal Interview with Theresa Davis, ECE. July 2014.