1. Program Design and Implementation – Problem Solving as a Process for Teaching Mathematics - 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. Exploring the relationship between societal and technological changes and teaching and learning mathematics through inquiry and math experiences 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 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 Spring 2010 SESSION 7 – May 5, 2010

2. Rough Agenda 5:30 – 6:15 6:15 – 6:35 6:35 – 7:05Focused Discussion Adolescent Development 7:15 – 7:45 7:45 – 9:00

3. Change - Learning Mathematics Through PS - Focusing on Communication and Interactive Learning PLAY … TAKE A RISK! Materials 2 dice, a pencil and paper How To Play Roll the dice and add up your score. Take as many turns as you like before you pass the dice. If the dice adds up to 7, you lose your score for that turn. If the dice adds up to 12, you lose your total score so far. All other numbers are safe. Who Wins First player to reach 99 What mathematics are you doing and learning? What is the student’s role? What is the teacher’s role?

4. Change - Learning Mathematics Through PS - Using Polya’s Problem Solving Process Make a Plan Take a Risk! How will you calculate and record all the scores? What strategies might you use? Carry Out The Plan Play the game. Record the scores in a graphic organizer. Keep track of the strategies you are using. Look Back Which strategies did you use that were successful or less successful? Why? How did you know when someone was about to win the game? What is the probability of winning 3 times in a row? How can you represent your data so that it looks like you are always winning?

5. The Mathematics – Probability

6. 3 – 2 – 1 Teaching through Problem Solving Write on a piece of paper you will be able to read from later… 3 – things that characterize Teaching through Problem Solving (“Structured PS” as per TIMSS) 2 – things that Teaching through Problem Solving is NOT! 1 – thing you want to learn about Teaching through Problem Solving

7. Teaching Through Problem Solving Many solutions to a problem by the students Working on a challenging new problem Students are doing the mathematics, rather than watching the teacher do it or listening to the teacher Students come to the board to post their solutions Teacher facilitate discussion to find the relationship between the solutions Providing a record of the discussion - see the progression of the work from the start of the lesson throughout Lessons and concepts were developed through examples, demonstrations (students), and discussions Using a chalkboard - to record the learning throughout the lesson - keep it recorded (keeps the attention over time, rather than on, off - keeps a record - to summarize learning - highlights/summary on the board Order the writing on the board important Building on previous day’s work - continuum of learning Students spend time inventing new ideas

8. 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 problem DURING (LESSON PROBLEM 20 min) Presenting and understanding the lesson problem Students working individually or in groups to solve a problem Students discussing solution methods AFTER (CONSOLIDATION the thing we think of as 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)

9. Criteria for a Problem Solving Lesson Content Elaboration- developed concepts through teacher and student discussion Nature of Math Content - rationale and reasoning used to derive understanding Who does the work Kind of mathematical work by students - equal time practising procedures and inventing new methods Content Coherence - mathematical relationships within lesson Making Connections - weaving together ideas and activities in the relationships between the learning goal and the lesson task made explicit by teachers Nature of Mathematics Learning - seeing new relationships between math ideas Nature of Learning first struggling to solve math problems − then participating in discussions about how to solve them hearing pros and cons, constructing connections between methods and problems − so they use their time to explore, invent, make mistakes, reflect, and receive needed information just in time

10. Teacher Inquiry - Annotated Bibliography 6 articles (one person), 8 articles (two people or more) 1st paragraph - describe key math idea 2 nd paragraph explains how you are using the key idea to design your lesson

11. Reading Strategies for Journal Articles Look for headings - to get an overview of what they are talking about - to skim through and highlight a couple of points (to remember what you read) Re-read the journal and look for those important ideas Look for structure - big idea of the article - go to the summary of the article first and the abstract Articulate or identify what the reading was focused on Capture it if it still sounds promising

12. Analytic journals Math Task 1 Math Task 2 Learning Theories paper Annotated Bibliography

13. What are the Range of Solutions for This Problem? 1. 2. What mathematics did we use in our solutions? 3. Record your ideas as a network (knowledge package), showing the interconnections among the curriculum expectations from grades 6 to 9. 4. What is the sorting criteria for these solutions?

14. Teacher Inquiry Topics Grade 9 Grade 8 Grade 7

15. Preparation for Saturday May 8, 2010 Treats: Margareta, Andrea, and David Reminder – Continue gathering math topic articles for teacher inquiry – Rationale due Sat May 5, (include change and Japanese instruction Start Reading … a. Describe 2 characteristics of each theory: behaviourism, constructivism, and complexity theory. b. Infer how these theories explain a mathematics teaching/learning experience. Behaviourism and Constructivism : - Funderstandings. Behaviourism, Constructivism (Piaget, Vygotsky) - Clements, D. & Battista, M. (1990). Constructivist learning and teaching. Arithmetic Teacher, 38(1), 34-35 Complexity Theory - Davis, B. (2005). Teacher as “consciousness of the collective’. Complicity: An International Journal of Complexity and Education, 2, pp. 85-88 - Davis, B. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education (34)2, pp. 137-167 Assignments