Practicum, Assessment, Evaluation, and Reporting in

OntarioIntermediate / Senior Mathematics Winter 2011SESSION 11 – Feb 2, 2011

Practicum

Practicum

Practicum

Practicum

What Can We Learn From TIMSS?Problem-Solving Lesson Design

BEFORE (ACTIVATING PROBLEM 10 min) • Activating prior knowledge; discussing previous days’

methods to solve a current day problemDURING (LESSON PROBLEM 20 min) • Presenting and understanding the lesson problem • Students working individually or in groups to solve a

problem• Students discussing solution methodsAFTER (CONSOLIDATION the REAL teaching 30 min) • Teacher coordinating discussion of the methods (accuracy,

efficiency, generalizability)• Teacher highlighting and summarizing key points• Individual student practise

(Stigler & Hiebert, 1999)

Compare your solutions. How are they similar? How are they different?

There are 36 children on school bus.There are 8 more boys than girls.How many boys? How many girls?

a) Solve this problem in 2 different ways. b) Show your work. Use a number line, square grid, picture,

graphic representation, table of values, algebraic expression

c) Explain your solutions. 1st numeric; 2nd algebraic

Bus Problem

There are 36 children on school bus.There are 8 more boys than girls.How many boys? How many girls?

a) Solve this problem in 2 different ways. b) Show your work.c) Explain your solutions using one or more operations.

What’s the Mathematical Relationship to the Previous Problem? …. Knowing MfT

Did you use this mathematical approach?

(Takahashi, 2003)

(Takahashi, 2003)

Did you use this mathematical approach?

Did you use this mathematical approach?

(Takahashi, 2003)

(Takahashi, 2003)

Did you use this mathematical approach?

(Takahashi, 2003)

Did you use this mathematical approach?

How are these algebraic solutions related to the other solutions? … Knowing Math on the Horizon

(Takahashi, 2003)

Which order would these solutions be shared for learning? Why? ... Knowing MfT

(Takahashi, 2003)

See WIKI

Return to ML Kestell

Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools. 2010

Seven Fundamental Principles – What do they mean for Mathematics Education?

Work with a partner and complete this form. Be specific about mathematics tools and strategies.

Assessment and Evaluation

Success Criteria based on Expectations

Assessment for and as Learning

On the WIKI: Instructional Strategies TIPS for Teachers

Mental Math• Addition (number lines, decomposing and composing)

− 8 + 5− 34 + 78− 392 + 259− 21.87 + 193.38

• Subtraction (number lines, compensation, alternative algorithms)− 32 – 18 − 363 – 149

• Multiplication (area model, lattice, halving and doubling)− 24 x 14− 36 x 17

• Division (subtraction algorithm, splitting)− 93 / 7− 260 / 13