1. Mathematics for Middle School Teachers: A Program of Activity- Based Courses Portland State University Nicole Rigelman Eva Thanheiser

2. What is the Mathematics for Middle School Teachers Program? Graduate Certificate Program & Undergraduate Minor Housed in mathematics department Relevance of the mathematics learned Activity based learning Discussion of children’s mathematical thinking

3. The certificate program consists of 8 courses: Computing in Mathematics for Middle School Teachers Experimental Probability and Statistics for Middle School Teachers Problem Solving for Middle School Teachers Geometry for Middle School Teachers Arithmetic and Algebraic Structures for Middle School Teachers Historical Topics in Mathematics for Middle School Teachers Concepts of Calculus for Middle School Teachers Teaching and Learning in the Middle School Mathematics Classroom

4. 200920102011201220132014 Winter MTH 4/593 MTH 4/590 MTH 4/591 MTH 4/594 MTH 4/592 MTH 4/595 Spring MTH 4/594 MTH 4/592 MTH 4/595 MTH 4/596 MTH 4/510 MTH 4/593 Summer MTH 4/591 MTH 4/592 MTH 4/510 MTH 4/593 MTH 4/594 MTH 4/595 MTH 4/590 MTH 4/592 MTH 4/596 MTH 4/591 MTH 4/595 MTH 4/510 MTH 4/593 MTH 4/594 MTH 4/596 MTH 4/590 MTH 4/592 MTH 4/510 Fall MTH 4/596 MTH 4/510 MTH 4/593 MTH 4/590 MTH 4/591 MTH 4/594 With careful planning it is possible to complete the program in 3 consecutive summers, 2 academic years and the intervening summer, or 3 academic years.

5. The graduate certificate admission requirements are: Completed B.A. or B.S. degree. GPA: 3.0 cumulative undergraduate, or 3.0 for upper division courses, or 3.0 in all graduate credit courses (a minimum of 12 credits). Completion of Mth 111 (College Algebra) and Mth 211 (Foundations of Elementary Mathematics I) or the equivalent.

6. Philosophy of the Graduate Middle School Certificate Program Problem solving activities that promote exploration and experimentation and which allow students to construct (and reconstruct) mathematical understanding and knowledge Development of multiple strategies or approaches to problems - discussing and listening to how others think about a concept, problem, or idea Small group work and cooperative learning Integration of children’s mathematical thinking Supportive and cooperative class environment

7. Discussion of Children’s Mathematical Thinking Connecting – Mathematics – Children’s mathematical thinking – Practice of teaching Activities – Interviewing children – Assessing whole classes – Viewing videos – Participating in Family Math Night

8. Example 4 ½ - 1 ½ – Solve the problem as many ways as you can – How could a 6 th grader justify 3 as an answer? – How could a 6 th grader justify 2 as an answer? – Show a video clip and make sense of the students’ reasoning

9. Example 4 ½ - 1 ½ – Solve the problem as many ways as you can – How could a 6 th grader justify 3 as an answer? – How could a 6 th grader justify 2 as an answer? – Show a video clip and make sense of the students’ reasoning

10. Example 4 ½ - 1 ½ – Solve the problem as many ways as you can – How could a 6 th grader justify 3 as an answer? – How could a 6 th grader justify 2 as an answer? – Show a video clip and make sense of the students’ reasoning

11. Justification for 4 ½ - 1 ½ = 2 S14-1 = 3 and ½ - ½ = 0 so the answer is 3

12. Justification for 4 ½ - 1 ½ = 2 S14-1 = 3 and ½ - ½ = 0 so the answer is 3 S2:“he did 4-1 was 3, and then he said the 2 halves don’t equal anything”

13. Justification for 4 ½ - 1 ½ = 2 S14-1 = 3 and ½ - ½ = 0 so the answer is 3 S2:“he did 4-1 was 3, and then he said the 2 halves don’t equal anything” S34-1 = 3 and ½ + ½ =1 and 3-1=2

14. Justification for 4 ½ - 1 ½ = 2 S14-1 = 3 and ½ - ½ = 0 so the answer is 3 S2:“he did 4-1 was 3, and then he said the 2 halves don’t equal anything” S34-1 = 3 and ½ + ½ =1 and 3-1=2 S4States you cannot combine ½ + ½ if you have 4 ½ - 1 ½ you don’t combine that

15. 4 ½ - 1 ½ = 2

16. Here’s the 4 by itself, no, ok, nobody’s ripped in half yet, its just them, so those 2 halves are taken out, so its 4 -1 is 3 and then they surgically clip that guy back together

17. 4 ½ - 1 ½ = 2 Here’s the 4 by itself, no, ok, nobody’s ripped in half yet, its just them, so those 2 halves are taken out, so its 4 -1 is 3 and then they surgically clip that guy back together

18. 4 ½ - 1 ½ = 2 Here’s the 4 by itself, no, ok, nobody’s ripped in half yet, its just them, so those 2 halves are taken out, so its 4 -1 is 3 and then they surgically clip that guy back together

19. 4 ½ - 1 ½ = 2 Here’s the 4 by itself, no, ok, nobody’s ripped in half yet, its just them, so those 2 halves are taken out, so its 4 -1 is 3 and then they surgically clip that guy back together

20. Use of video clip Address: – Models of subtraction and their representation Take away vs. comparison – Fractions How do students think about fractions? How do students think about mixed numbers? – Appropriate models for a context – What do teachers need to know? To understand student thinking To build on student thinking to facilitate class discussion

21. Why does it work? Preservice & In-service teachers working together Exploration of mathematics in small groups Connection to “real” children’s mathematical thinking Relevance

22. Student Quotes I really have enjoyed the class discussions and activities. These were very amazing to me as it has really helped me to experience looking at and analyzing others approaches to problems that I may not have seen or even been able to understand at first glance. Even though they are hard to schedule, I have learned a lot from the student interviews. Seldom do we have the chance to sit down with one child for 45 minutes and explore their mathematical thinking. This has been a small luxury and very illuminating.

23. Secondary Mathematics Methods Develop views about how adolescents learn mathematics and how to facilitate learning via the tasks posed, the classroom norms established, the questions asked, etc. Analyze and adapt tasks/lessons and plan for implementation that promotes high level thinking and reasoning for each student. – Apply learning from course in the field experience. – Navigate different points of view about teaching and learning. – Reflect critically on developing instructional practice.

24. Course Structure Engage in mathematical tasks as learners. Examine student work and students at work (video and written cases). Discuss teacher moves that facilitate learning both as modeled by the instructor and as modeled in the classroom cases.

25. Course Projects Analyzing Classroom Talk Plan and teach a lesson. Then analyze a transcript of the classroom talk for – the types of questions asked and the purposes they served, – the student understanding evidenced in student responses, and – the role questions play in student learning.

26. Course Projects Lesson Study Collaborate with 1-2 others to create a mini-unit that reflects the learning from – the readings, – class discussion, and – other teaching/learning settings about Standards-based instructional practices.

27. Course Projects Video Analysis An opportunity to plan, implement and reflect deeply on teaching. Analysis draws upon evidence from the video and includes – intended and actual student mathematical learning, – ways the teacher supported or inhibited student, and – teacher candidate learning and implications.