Teaching Through Problem Solving – Bermuda Framework for Teaching Mathematics Gilbert Institute Ongoing PD commencing the week of March 3, 2014 Rebeka Matthews Sousa Instructional Facilitator for Mathematics rsousa@moed.bm

In this Session, teachers will: Consider the shifts in classroom teaching Engage in Mathematics Lesson, which demonstrates the Framework for Teaching Mathematics Discuss and Reflect on the Framework (Three-Part Lesson)

Shifts in Classroom Practice In the Mathematics Education world, we have undergone huge paradigm shifts. The classroom in which we were students of is no longer what is consider exceptional teaching Why the shift? – we don’t just want our students to be good at school math, but we want them to be able to apply what they know to real world examples and context. This requires many skills as mention previously (our process skills) You will now have a moment to reflect the shifts needed in the classroom. The types of learners may or may not have changed – that is up for debate, however, what we expect of them as learners has changed.

Mathematics Education Reform Problem Solving,  Reasoning and Proof,  Communication,  Connections, and  Representation All highlight ways of acquiring content knowledge Student Expectations for doing Mathematics Shifts in Classroom Practice Teaching Skills require Its not just about reading and arithmetic anymore. Major mathematics education reform have considered that our students do not just need to be good in school mathematics, but there are other skills that they require. Our students must be able to collaborate and discuss, communicate reasoning, problem solving and ultimately THINK This requires shifts in classroom practice, which includes new teaching skills. The mathematics classroom today looks very different than the mathematics classroom we experienced as students. Math is not just about the right answer or one procedure to determine a computation, but about a balance of skils including computation and mental math skills as well as communication, justification and reasoning and problem solving. In the Cambridge Curriculum and Planning documents it specifies that the problem solving it not to be taught in isolation, but taught throughout the curriculum strands. So do we make this happen? Which problem solving strands would apply to the Fixed volume task. includes

Cambridge Objectives Mathematicians will: 5Gs1 Identify and describe properties of triangles and classify as isosceles, equilateral or scalene. 5Ps7 Identify simple relationships between shapes, e.g. these triangles are all isosceles because … 5Ps9 Explain methods and justify reasoning orally and in writing; make hypotheses and test them out Materials needed: chart paper, triangles, rulers, compasses, protractor,

Triangles Triangle Sort Sort the entire collection into three groups so that no triangle belongs to two groups. Give a description or name to each of the groups and record on chart paper. Once you have found one criterion for sorting. Determine a second. In groups of 2-4

Cooperative Learning Groups & Responsibilities LS P6 Group Leader Materials Manager Task Manager Recorder Liaison between group and teacher Group speaker Collects and returns all materials for group Ensure all members are participating, on task, and keeps track of time. Records all information necessary on chart paper to reflect participants thoughts and ideas

Reflection How did you sort the triangles? Which categories or descriptions did you use?

Summarizing Triangles The following shows how triangles can be classified according to some of their features: ANGLES, SIDES, SIZE Chart description on separate paper: Angles, Size, Length

Summarizing Triangles The following shows how triangles can be classified according to some of their features: ANGLES, SIDES, SIZE Chart description on separate paper: Angles, Size, Length

Exit Card In your own words, write your own description of each of these types of triangles. Draw a diagram of each – using a ruler! Triangle Description Diagram Scalene Isosceles Equilateral

Extension Sketch a triangle in each of the nine cells. Of the nine cells in the chart, two of them are impossible to fill. Can you tell which ones and why? “Triangle sort” results in definitions of the six different types of triangles without having to list these definitions and have you memorize them.

Teacher Reflection What were some of the components of this lesson? Consider the Rubric for Quality Teaching in Mathematics, which components of the rubric were met during this lesson? Why use the three-part lesson or teaching through problem solving framework to teach mathematics? How do I make this part of my everyday math lesson? Or how do I find resources to continue teaching this way? Strategies Critical Thinking Justification and evaluation Communication

Triangle Sort Lesson Plan

Instructional Approaches Teacher Directed Student Practice Problem Solving - Application Problem Solving Scenario or Task Student Discovery Teacher Facilitated Sharing The Flipped classroom The Traditional Approach Teacher Centred The Three-Part Model Student Centred

What are some elements of the teaching through problem-solving/inquiry based framework? Three-parts Teacher could… Student Role BEFORE Engage “Activate thinking” Launch Task. Model manipulatives Solve a similar/simpler problem with the students Think about the problem. Ask questions for clarification. DURING Teaching through Problem Solving   Students “doing” Mathematics Using questioning and prompting to guide students, but not giving solution. Ask about the strategies they are using and why they have selected them? Working through the problem. Using manipulatives and various strategies. AFTER Reflect and Connect “Share time” Addresses misconceptions and facilitates discussion based on student responses. Direct instruction. Student shares ideas, through process Reflect on the lesson 5 mins What do you think is the most challenging part for teachers? “letting go” What task do I choose? What are the types of questions do I ask? – Give questions cards

Reading from Chapter 2 Teaching Through Problem Solving Introductory Paragraphs – p13-17 Text & ISBN Title Authors Year Level recommended ISBN-13:  978-0132824828 Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades Pre K-2 (Volume I) (2nd Edition) John A. Van de Walle, Lou Ann H. Lovin, Karen H Karp, Jennifer M. Bay Williams P1-P3 978-0132824873  Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II) (2nd Edition)   John A. Van de Walle, Karen S. Karp, Lou Ann H. Lovin, Jennifer M. Bay-Williams  P4-P6 *P3 may choose this book instead of Volume 1

Reflection (Three-Part Lesson) Explain in your own words, the phases of the three-part lesson. Explain the three-parts based on the lesson you experienced last week. Which

Teaching Through Problem Solving Referring to the Shifts in Classroom Practices How does the three-part model for teaching support these shifts in classroom practices? Jot down on sticky Place on board

Why Problem-Solving/Inquiry based Lessons? It’s a comprehensive learning/teaching structure that: Supports the delivery of curriculum Is based on the problem solving model Promotes conceptual mathematical understandings Promotes 21st Century Learning Skills Allows for differentiated instruction Is consistent with independent skills being demonstrated in the mathematics processes (e.g. problem solving, reasoning and proving, reflecting, tool and strategy selection, making connections, representing understanding and communication) Allows students to get the “BIG IDEAS” or the fundamental principles of mathematics that link the specifics Promotes collaboration

A Mathematics Framework Based on the Balance Math Program DO NOW / Math Review Three Part Lesson 1. Activate 2. Working On it 3. Reflect and Connect Mental Math

Reflection (Three-Part Lesson) What do you see as the benefits of teaching this way? What additional questions do you have with regards to the Mathematics Framework for Teaching (Three-Part Lesson) What can you do in your lessons to encourage mathematical thinking and reasoning? How can the three-part framework assist in structuring such lessons?

Reflection How do I make this part of my everyday math lesson? Or how do I find resources to continue teaching this way?