Inquirying About Learning Mathematics for Teaching

- Exploring relationships between participants’ teaching and learning mathematics experiences, beliefs; mathematics content knowledge and mathematics pedagogy within an inquiry and research framework - Making sense of embodied knowledge of mathematics through different data management strategies.• Understanding and implementing Ministry of Education curriculum expectations and Ministry of Education and district school board policies and guidelines related to the adolescent • Demonstrating an openness to innovation and change• Having the theoretical understanding and foundation necessary to design, implement and assess programs for the adolescent learner

ABQ Intermediate Mathematics Winter 2010SESSION 2 – January 13, 2010

What are we learning in this ABQ Int Math Course? … Scavenger Hunt

• 1 - 4• 5 - 8• 9 - 12• Post your questions …

• Talk in group respond to 4 questions

• Pass papers counterclockwise review the answers of the other group and make sure you understand it the same way…

• Questions on board…

What are we learning in this ABQ Int Math Course? … Scavenger Hunt

See sheet complete and uploaded to our wiki

Teacher Inquiry Plan

Key information- grade level- number of students- math content- time lines - can work in pairs or triads- topic might change (but do so in the next week or so)

- Do the lesson plans by Feb 3 bring questions for colleagues to do (or Feb 10 – when teaching?)- Data collection and lesson plan analysis data Feb 24

Due Saturday Jan 16

RequirementsLOG 60 h expectedCurriculum

6

• Expert personal knowledge of mathematics is ironically inadequate for teaching elementary students mathematics.

• Effective teachers must be able to work backward from their own mature and compressed mathematics content knowledge and unpack its core elements.

• Effective teachers enable students to access new mathematical ideas accessible to students through their own thinking and construction.

• Effective teachers work with the mathematics that students present, often in an unfinished, yet growing state.

(Ball, 2005)

Learning Mathematics for Teaching

Work of Mathematics Teaching• Sequencing of math content and curriculum

materials• Generating and using strategic examples and

multiple representations• Talking mathematics and having students talk• Understanding and analyzing multiple solutions• Evaluating the mathematical significance of

students’ comments and coordinating discussion for learning

• Building correspondence between mathematical ideas, models, and symbols

Why Solve it in More than 1 Way… Isn’t the Answer Enough?

What different strategies could be used to determine 85% of 60?1. Describe strategies that you

would use to determine 85% of 60?

2. Explain the kinds of mathematics that is needed to determine the different ways to calculate 85% of 60.

One Solution per one page (landscape orientation)

85% of 60 = ?

85% of 60 = ?

Math Task 11. Show 4 different solutions (gr 6, 7, 8) to the problem.2. Identify the curriculum expectations evident in each solution.3. Which solution will you have the student share first, second, third,

and fourth? Why?4. Describe how the solutions are mathematically related to one

another.

8-1/2”

11” + 11”

Solution 1 Solution 2 Solution 3 Solution 4

Gr6 Gr6 Gr7 Gr8expectation(s) expectation(s) expectation(s) expectation(s)

Describe mathematical relationships between solutions

Strategy title Strategy title Strategy title Strategy title

AFTER - Consolidation

Math Task 1

Preparation:

1. Record the curriculum expectations to be demonstrated by the students (gr 6, 7, 8) .

2. Show 4 different solutions to the problem.3. Which solution will you have the student share first,

second, third, and fourth? Why?4. Describe how the solutions are mathematically related to

one another.

For Saturday, Jan 16, 2010TREATS: Cory-Ann, Rashi, AdrianaREAD AND RECORD: (Read 2 of the 4

articles on change.)A. Be prepared to describe 2 ideas

about changes needed in mathematics education. (Pick quotes from any of the 4 articles.)

B. Be prepared to make inferences about how the changes impact teaching and student learning of mathematics.

TEACHER INQUIRY PROJECT

C. Teacher Inquiry Plan due

• Ball, D., Hill, H., and Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade and how can we decide? American Educator, pp. 14-17, 20-22, 43-46.

• Cohen, D. & Ball, D. (2001). Making change: Instruction and its improvement. Phi Delta Kappan. pp. 73-77.

• Battista, M. (1999). The mathematical miseducation of America’s youth. Phi Delta Kappan Online. http://www.pdkintl.org/kappan/kbat9902.htm. pp. 1-15.

• Wilms, W. (2003). Altering the structure and culture of American public schools. Phi Delta Kappan Online. http://www.pdkintl.org/kappan/k0304wil.htm.