Analyzing Program Design and Implementation through Mathematics Learning Theory - Exploring Representations of Addition and Subtraction – Concepts, Algorithms, and Mental Math - Exploring Algebraic Reasoning through Arithmetic, Geometry, and Data Management using manipulatives and graphing calculators - Relating theories of learning and adolescence, lesson design principles, and components of an effective learning environment for effective mathematics teaching of adolescent students Creating learning environments to support adolescent students in learning mathematics Creating learning environments conducive to the intellectual, social, emotional, physical, linguistic, cultural, spiritual and moral development of the adolescent Understanding and implementing Ministry of Education curriculum expectations and Ministry of Education and district school board policies and guidelines related to the adolescent ABQ Intermediate Mathematics Spring 2011 SESSION 7 – May 18, 2011

Preparation for May 18, 2011 (6:00-9:30) Treats : Sherri and Rajesh Read and Be Prepared to Respond: Constructivism (Piaget, Vygotsky) and Behaviourism: A. Describe 2 characteristics of Constructivism (Piaget, Vygotsky) and Behaviourism learning theories. B. Infer how they relate to mathematics teaching and learning through problem solving. Teacher Inquiry: - Researching journals for math content - Designing series of 3 mathematics lessons Assignments DUE -overdueTechnology Webquest -May 25 – lesson plan analysis -May 28 – Annotated Bibliography -June 1 – learning theories paper

Improving Journal Writing Include introductory statement that identifies the purpose and focus of your journal entry Think of journal entry as an argument (e.g., explaining how characteristics of adolescent learning relate to teaching and learning mathematics through problem solving) Avoid general statements or statements that are not specific in detail and related to the purpose and focus of the journal entry Intersperse inference to t/l math through problem solving right after characteristics of adolescence Include mathematical details (not just a vague description of the events surrounding the mathematics we did) Conclusion should describe the argument details, not new details 1 Characteristic, explanation, inference, math example

Constructivism - Piagetian Characteristics Teaching and Learning Mathematics Through PS

Social Constructivism (Vygotsky) Characteristics Inferences on Teaching and Learning Through PS

Behaviourism (Skinner) Characteristics Inferences on Teaching and Learning Through PS

Analytic Journal Writing Talk, Write, Talk (Use article in your writing.) A. Describe 1 characteristics each for Piagetian, Constructivism, Social Constructivism, and Behaviourism B. Infer how they relate to mathematics teaching and learning through problem solving. C. Include a mathematics example as evidence for your idea. 1. Funderstandings. (2008). Behaviourism, Brain-Based Learning, Communities of Practice, Maslow’s Hierarchy of Needs, Piaget, Vygotsky and Social Cognition. Retrieved from m/about_learning.cfm. pp m/about_learning.cfm Own research APA Format: Direct quote - Ball, Hill, and Bass (2005) explains that “ ” (p. ). Indirect quote - Ball, Hill, and Bass (2005) explains that <paraphrase of what they said

Teacher Inquiry - Annotated Bibliography 4 articles 1st paragraph - key math idea in the article related to your TI 2 nd paragraph - explains how you are or are not using the info from the journal article to design your lesson and why DUE – May 28 Literature review and primary research – research question Primary research – secondary question

Analytic journals TI plan Math Task 1 Math Task 2 Learning Theories paper Annotated Bibliography

Learning Theories Paper (Smaller) Describe one of your TI math lessons learning goal (expectations), the student learning tasks (Before (activation task), During (lesson problem), Practice (practice problem)) Learning tools - manipulatives you will provide for students Strategies that you will use to implement the lesson (e.g., cooperative learning strategies - think-pair-share, turn and talk, graffiti; gallery walk; math congress) – KKZ to produce Analyse the lesson in terms of learning theories: adolescent learning, communities of practice, Maslow’s Hierachy, constructivism, social constructivism, behaviourism, complexity theory to justify the design of this theory

Growing Dot Problem Solve in 2 different ways. Record one solution per 8-1/2” x 11” paper. Use marker.

Compare to bansho plan

Exploring Whole Number and Decimal Addition and Subtraction

Integer Addition and Subtraction (+2) 5.+4 – (+2) (-2)6.+4 – (-2) (+2)7.- 4 – (+2) (-2)8.- 4 – (-2) a. Show using 2 colour counters. b. Show using a number line. How does the idea of part-whole relationships, compose/join and separate/decompose related to integer operations?

Topic Discussions - Schedule & Readings Adolescent Learning (BLUE) Communities of Practice, Maslow’s Hierarchy of Needs (RED) Behaviourism, Constructivism (PURPLE) Complexity theory (KKZ) Adolescent Learning (2) Jenson, E. (1998). How Julie’s brain learns. Educational Leadership, (56)3, pp E - Knowles, T. and Brown, Dd. (2000). Understanding the young adolescent. What every middle school teacher should know. Portsmouth, NH: Heinemann. pp (1) Reinhart, S. (2000). Never say anything a kid can say. Mathematics Teaching in the Middle School. Pp (3) Stahl. R. (1994). Using think-time and wait-time skilfully in the classroom. ERIC Clearinghouse of Social Studies Social Science Education. Bloomington, IN., pp Communities of Practice - Funderstandings, Wenger, internet search Maslow’s Hierarchy of Needs – Funderstandings, internet search Constructivism (Piagetian, Vygostkian) Clements, D. & Battista, M. (1990). Constructivist learning and teaching. Arithmetic Teacher, 38(1), Funderstandings, Internet Search Complexity Theory Davis, B. (2005). Teacher as “consciousness of the collective’. Complicity: An International Journal of Complexity and Education, 2, pp Davis, B. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education (34)2, pp Topic Discussion Process 30 minutes 1 facilitator per 2 colleagues (one from each of the other groups) Preparation (by all) - do the readings, and website search Facilitator - develops some thought-provoking questions or task to stimulate discussion of the topic, making reference to preparation Colleagues - participate in task to be prepared to share learning with group members in record learning in journal

Preparation for May 25, 2011 (6:00-9:30) Treats : Flora Read and Be Prepared to Respond: Complexity Theory: A. Describe each condition of a complexity learning theory. B. Infer how they relate to mathematics teaching and learning through problem solving. Davis, B. (2005). Teacher as “consciousness of the collective’. Complicity: An International Journal of Complexity and Education, 2, pp Davis, B. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education (34)2, pp Teacher Inquiry: - Researching journals for math content Assignments DUE -overdueTechnology Webquest -May 25 – lesson plan analysis -May 28 – Annotated Bibliography -June 1 – learning theories paper