Resources for Teaching Elementary Math Methods

1. Resources for Teaching Elementary Math Methods Preservice Teachers Seeing and Sharing Mathematical Thinking… …of Students and …in Communities Corey, Beth, and Jenna from ISU MMGG 2006

2. Adler (2000, p. 207) stresses the need to shift focus from Material to Human Resources “…mathematics teacher education programmes need to work with teachers to extend common-sense notions of resources beyond material objects and include human and cultural resources such as language and time…” MMGG 2006

3. Teacher EQUITY Student Mathematics USE Student Curriculum Technology Manipulatives Parents and Families Community Resource Framework for Elementary Mathematics MMGG 2006

4. Interviews- Developing Them as we Learn CGI – after class, during class Interviews- teachers with other teachers to test my own knowledge of strategies Interviews – with home school children/parents To test my ability to identify strategies kids use To connect to parents and the community beyond schools Use Interviews in Practicum To inform my lesson plans To learn about and modify “high,low” kids, To “see” learning (content/attitudes) after lesson The Now: Focusing on the ‘inner circle’ (teacher-student-mathematics) MMGG 2006

5. Assessment framework: Content, Processes, and Attitudes (Cantlon, 1994) CGI: further clarifies content and processes as they relate to whole number operations Working with small groups of children in practicum setting 2-5 interviews, audio-taped Reflective journals One child to focus on, case study to teacher and methods instructor What’s next: Focusing on the ‘inner circle’ (teacher-student-mathematics) MMGG 2006

6. Reflective Journals: 4 parts see handout • Part A: Mathematical tasks • identifying content ideas, justifying the next set of problems they will use, etc. • Part B: Children’s thinking • collect data on children’s developing mathematicalcontent understandings, processes, and attitudes • Part C: Thinking about their own role in the interaction • Part D: Miscellaneous • questions raised, interesting things noticed, etc. MMGG 2006

7. Data and Analyses • Data: • 2 cohorts of preservice teachers, n = 21 & 22 (3 chose not to participate) • Fall, 70 journals analyzed • Spring, 42 journals analyzed • Analyses Focused on: • The “forms” of reflection related to mathematical content MMGG 2006

8. Q1: What mathematical ideas did your problems contain? MMGG 2006

9. Q2: Based on what you’ve heard in the interview, what might you do next? Why? • Mathematical Content-Related Responses: • how to change numbers (e.g., smaller number in ones place) and problem structures (e.g., JRU vs. JCU) • make problems related (e.g., subtr/div; add/multipl) • Content/Process-Related Responses: • “…single digits are getting too easy because they are oftenusing derived facts, so we’re going to use numbers between 10 and 20” • Also had responses that focused on • processes (e.g., getting children to communicate or listen better), • attitudes (e.g., working together better, building confidence), • or emotions (e.g., not letting students get frustrated, upset, or bored) • PRACTICE – common reason for continuing same problem MMGG 2006

10. Q3: What do you see as this child’s strengths with respect to number and operation after today’s interview? What do they need to develop further? Provide evidence for your claims. • Claims sometimes too vague • “R is really understanding everything that we pose for him. He tries all of the problems w/out hesitation…” • “J’s strengths is he knows the basics of math…” • Did not provide sufficientevidence for claims made • “Weakness is that he doesn’t understand place value.” • Restated items about processes, but did not say what they thought that meant to mathematicalcontent understandings • “…She would not talk to other students who were being loud and she would say to herself 4+4 = 8 and 4 equals 12, three 4’s is 12…” • Often focused on attitudes • “Frustrates easily. If prob doesn’t make sense, he gives up” • “J had a hard day. He was not in a working mood…” MMGG 2006

11. Part C: Thinking about their own role in the interaction • Mathematical task framework (QUASAR) • Levels of questions and types of student responses • When and how they interrupt and/or assist • Funds of Knowledge… MMGG 2006

12. How else can we help students learn about families and communities and LINK that learning to what they’ve learned about student thinking? MMGG 2006

13. Teacher EQUITY Student Mathematics USE Student Curriculum Technology Manipulatives Parents and Families Community Moving out in the “circles”…. MMGG 2006

14. The Community Resource Poster Project • “As we were doing this activity, I began to realize that you could go almost anywhere and put together a lesson that involves math…a great way to integrate real life math with classroom learning.” • GREAT! Yet, there are some interesting issues and questions…. MMGG 2006

15. Value of resources is neither unambiguous nor automatic MMGG 2006

16. Types of resources “vs.” use of resources MMGG 2006

17. How can these kinds of activities be better integrated with the “core content” of elementary mathematics? MMGG 2006