(-Christina Mete)2 + (Kathryn Mitchell)/2 + (Kyle Duelund)3 + (Mike Seccareccia)! +

d/dx(Stephen McCarthy) + (Andrew Iacobo)c2 + ((Marco Fiore)/x) + C =

The Math Group!

Learning Objectives

• By the end of this presentation, the class should know:– What a situational problem is and how it fits

within the idea of authentic assessment.– How they might adapt situational problems to

practice authentic assessment in their own fields.

Math assessments are more than just crunching numbers!

We should help students to:• Solve problems of

everyday life• Participate intelligently

in civic affairs• Be prepared for jobs,

vocations, or professions

We need assessments to:

• Focus on conceptual insights and analytical skills

• Feed back into learning• Require a variety of skills

Authentic Assessment

“An assessment task that mimics real-world experiences by assigning students real-life roles and engaging them in contexts as similar as possible to those encountered in the world beyond the classroom.”

(Cooper, 2007)

What do math teachers assess?

Two mathematic-specific competencies:1) Solves a situational problem (C1)2) Uses mathematical reasoning (C2)

What is a “situational problem”?(the QEP’s perspective)

A situational problem:• Is the main part to both math and everyday activities.• Is an instructional tool.• Is a process in and of itself.

Chapter 6Mathematics, Science and Technology

What is a “situational problem”?(the students’ perspective)

It is a problem:

• They have never encountered in class before.

• Whose solutions require the use of a new combination of rules or principles that they may or may not have been previously learned!

Situational Problems, a 4-dimensional problem:

1) Thinking and Reasoning: Gathering data, exploring, investigating, interpreting, reasoning, modelling,

designing, analyzing, formulating hypotheses, using trial and error, generalizing, and checking solutions.

2) Settings: Working individually or in groups.

3) Mathematical Tools: Using symbols, tables, graphs, drawings, calculators, computers,and manipulatives.

4)Attitudes and Dispositions: Including persistence, self-regulation and reflection, participation, and enthusiasm.

BOLD = AWESOME/EMPHASIZED BY THE REFORM

Situational problem example

Evaluation of Situational Problems(according to the QEP)

• Oral or written explanation student understanding

• Mobilization of mathematical knowledge

• Development/explanation of solution

• THE RUBRIC

Evaluation: Pros and Cons

The Rubric

Pros: - “Holistic” approach. - Sets a standard less subjectivity equal marking.

Cons: - Less precision on a ‘per step’ basis. - Subjectivity is sometimes needed.

Fair vs. Equal?

Rubric for marking situational problems

Situational problems &authentic assessment

Plus Minus Interesting

Students construct their own responses instead of choosing a single answer.

Strong focus on reading comprehension, in addition to mathematics.

There can be multiple solutions to the same question.

Students are encouraged to solve problems in many ways.

Difficult to prepare students for such a problem.

Large question based on one theme.

Problem represents real life situations.

Difficult for teachers to correct.

No suggestion as to where to start with the problem.

Difficult for teachers to create.

Should situational problems be used to assess students?

-4

+4-2

+5

-3 -2

0+3

-2

+1

Net Score: 0

0

Students can discuss their solutions outside of class.

Group discussion5 minutes in groups,then share with class

Discussion prompt: how could you apply situational problems in your field?

• Recall, a situational problem:• Represents a real-life situation.• Presents something new to students.• Requires students to use a combination of

information or principles in a new way.

Question #1

A situational problem would be a great way to assess which learning objective?

A) rote learning B) knowing the quadratic equation

C) applying mathematical knowledge to real lifeD) how many sides in a triangleE) none of the aboveF) all of the aboveG) C and EH) Why have I read this far down the list?

Question #2

Situational Problems are:A) Easy to correctB) Short in lengthC) Easy and fun to prepare students forD) Always have one possible answerE) None of the aboveF) All of the above

Question #3

True or false?

• Situational problems are a perfect example of authentic assessment.

False.

Question #4

True or false?

• All math teachers agree that rubrics are the best way to evaluate situational problems.

False.

Question #5

Fill in the blank:

A way to assess real-life applications of knowledge in mathematics is by using a ___________________________.Situational problem

The End!

Any questions for us?

References

• Cooper, D. (2007). Talk About Assessment: Strategies and Tools to Improve Learning. Canada: Nelson Education Limited

• Pandey, T. (1990). Authentic Mathematics Assessment. ERIC/TM Digest. 1-3. Retrieved from http://www.eric.ed.gov/ERICWebPortal/contentdelivery/servlet/ERICServlet?accno=ED354245

• QEP, (2004). Ch.6 Mathematics, Science and Technology: Cycle 1. Retrieved from http://www.mels.gouv.qc.ca/sections/programmeFormation/secondaire1/pdf/chapter61.pdf

• QEP, (2009). Mathematics: Cycle 2. Retrieved from http://www.mels.gouv.qc.ca/sections/programmeFormation/secondaire2/medias/en/Mathematique_SecondVersion_a.pdf