Mathematics Professional Learning Menu: Effective Use of Learning Tools: Day 1

CEC Monday, April 16th 2012

A Prayer for Math Teachers:Lord, as we gather here today, we pray for your guidance…

You were there when Jesus multiplied the loaves and fishes, and when Moses divided the Red Sea.

We ask that you be with us now.

Help us trust that your highest power will be our guide.

Help us to be a positive influence on our students.

Help us to be a fraction of the teacher Jesus was.

Help us to recognize the infinite possibilities that are born of faith.

Amen

Agenda Learning Goals Catholic Board Learning Plan (CBLP) 2010-2013

Minds On: Graffiti 3-Part Lessons Representation using a math tool (manipulative) Creating a question

Action: Intermediate Concepts Using Manipulatives Expert Groups-Jigsaw Using the TIPS2.0 Template Planning Time

Consolidation: Next Steps and Closing Thoughts Homework/Dismissal

Learning Goals:

Deepen your understanding of 3-Part Lessons and the foundational principles in the CBLP

Co-plan a 3-Part Lesson that uses a manipulative

Catholic Board Learning Plan (CBLP) 2010-2013 SMART Goal: Increasing student achievement on EQAO

assessments (3, 6 & 9) by 5% by 2013 Foundational Principles:

Ontario Curriculum and ministry support documents are the primary sources for all mathematics instruction.

The mathematical processes described in the Ontario Curriculum are used throughout all mathematics instruction.

A minimum of 60 minutes is provided daily for mathematical instruction. The diverse learning needs of EACH student are supported by mathematical

instruction, assessment and evaluation that are varied in nature and provide multiple opportunities to demonstrate learning.

The comprehensive list of strategies that relate to effective mathematics instruction are used regularly.

Expected Practice: By June 2013, all mathematics instruction will be delivered using a 3-part lesson model

Connections to CBLP

Minds On…

Graffiti 3-Part Lesson Framework

Each group will receive a chart paper with one of the 3 parts (either teacher or student actions) of the lesson framework

Using your group’s coloured marker, you are write one or two characteristic(s) about the topic on the chart paper

For each rotation your group will add to the list Once you have rotated through return to your

starting point and be prepared to share with the whole group

Representing Using Manipulatives

Using the math tools in front of you represent in as many was as you can:

OR any fraction of your choice

Teacher Questioning Create a question or task that the answer is the

fraction that you chose from the previous task.

Be prepared to share.

Make sure that the question/task allows the use of manipulatives.

Parallel Tasks and Open Questions

Parallel tasks are sets of tasks, usually two or three, that are designed to meet the need of students at different developmental levels, but that get at the same idea or concept.

Open questions are broad-based questions with many appropriate responses or approaches; the questions serve as a vehicle for differentiating instruction. Allows students at different developmental levels to succeed even when responding differently.

BREAK TIME!

Action …

Jigsaw Activity

Each person in the home group will choose one of the manipulatives which will establish their expert group.

In your expert group, show how you could teach as many of the concepts on the list using your math tool (manipulative).

Be prepared to teach back at your home group.

Intermediate Manipulatives Concepts  1. Addition and subtraction of fractions. 2. Multiplication and divisions of fractions. 3. Addition and subtraction of integers. 4. Multiplication and divisions of integers. 5. Determine, through investigation the angle relationships for interesting lines. 6. Determine, through investigation the angle relationships for parallel lines and

transversals. 7. Determine, through investigation the sum of the angles of a triangle. 8. Determine, through investigation and describe the properties and relationships

of the interior and exterior angles of triangles, quadrilaterals, and other polygons. 9. Represent growing linear pattern. 10. Represent rate of change. 11. Solving one variable equations. 12. Simplifying one variable algebraic expressions. 13. Expanding one variable algebraic expressions. 14. Factoring one variable algebraic expressions. 15. Perimeter of two-dimensional shapes. 16. Surface area of three-dimensional objects. 17. Volume of three-dimensional objects. 18. Describe the relationship between the algebraic and geometric representations

of a single-variable term up to degree three. 19. Illustrate equivalent ratios. 20. Solve for the unknown value in a proportion. 21. Determine through investigation relationships among area, perimeter,

corresponding side lengths, and corresponding side angles of similar shapes. 22. Determine through investigation relationships among area, perimeter,

corresponding side lengths, and corresponding side angles of congruent shapes. 23. Distinguish between and compare similar shapes and congruent shapes.

Learning Tools

Learning tools for Mathematics can be either: Concrete (manipulatives) Virtual (technology)

Learning tools have been used in mathematics instruction since the 1960s and research has measured their impact.

The Research Says … A focus on deep learning of particular mathematics topics –

through a variety of strategies, including working with concrete materials – leads to greater conceptual depth (Ben-Chaim, Fey, Fitzgerald, Benedetto, & Miller, 1998; Fletcher, Hope, & Wagner, 2001; Siemon et al., 2001).

Manipulatives allow students to concretely explore mathematical relationships that will later be translated into symbolic form. The key to the successful use of manipulatives lies in the bridge – which must be built by the teacher – between the artifact and the underlying mathematical concepts (D’Ambrosio et al., 1993). The mathematics is in the connections, not the objects (Kilpatrick & Swafford, 2002).

Leading Math Success, 2004

The Research Says Studies on the use of manipulatives by students

described as low achievers, at risk, having behaviour problems, or with limited English proficiency have found positive effects on achievement (Ruzic & O’Connell, 2004).

Even at the secondary level, manipulatives are necessary tools for supporting the effective learning of mathematics. … By analysing students’ concrete representations of mathematical concepts and listening carefully to their reasoning, teachers can gain useful insights into students’ thinking and provide supports to help enhance their thinking (Grade 9&10 Curriculum Document, p23)

Document Camera The surprising insights

The Questions about….. What are the manipulatives…… Where do I get them……..

Effective Classroom Strategies for Using Manipulatives In your group,

discuss the strategies outlined on the Manipulatives Management handout

Share any additional strategies

Questions? Comments

LUNCH

Bless us, O Lord, and these your gifts, which we are about to receive from your bounty. Through Christ our Lord.

Amen.

Using the TIPS 2.0 Template

This template allows you to plan a 3-part lesson

The lessons have embedded literacy, DI and assessment startegies

Co-Plan a Lesson Form groups of 2 or 3 teachers of

the same grade/course Plan a three part lesson for a

concept everyone in the group will teach between now and May 1st

The lesson must feature the use of a learning tool and bring student work to be shared

You are encouraged to use literacy, DI and assessment strategies

Consolidation/ Debrief …

Manipulatives Wiki Resources

(http://dpcdsb-math-stuff.wikispaces.com/) Click on DPCDSB Wikis (on the left) Click on Manipulatives link

There are three pages on the wiki: Home Page: General information Math Menu: Resources from sessions Ministry: Resources and research on Manipulatives

Visit the site often to see new resources If you discover a useful resource, send it to us and

I’ll post it.

Closing Thoughts:

The most influential factor in improving student achievement is not

demographics, socio-economic status, or classroom resources, but rather

more effective teaching!

Robert J. Marzano, Classroom Instruction that Works, 2001

Closing Thoughts:

It is only natural for me to wantthem to be successful, but by

merely telling them the answers, doing things for them, or showing

them shortcuts, I relieve students of their responsibilities and deprive them of the opportunity to make

sense of the mathematics they arelearning.

Homework / Dismissal Teach the lesson you

planned and come prepared to share the experience on May 1st session

Bring students artifacts Have your lesson on USB or

bring your computer Complete an exit ticket

before you go Questions? Comments

For more information, please contact us:

Susanna Martellacci– Mathematical Literacy Consultant (7-10) x 24373

Dorota Jakubowska – Mathematical Literacy Consultant (7-12) x24188