Advancing Mathematics Education Through Collaborative Research

1. Improving Teaching and Learning through Professional Development A Collaborative Research Project involving AAAS Project 2061 Texas A&M University University of Delaware School districts in Delaware and Texas

2. Research Question • What is the relationship between the use of research-based instructional strategies and student learning of specific mathematics ideas and skills?

3. Logic Model TeacherPractice Professional Development + Curriculum Material Teacher Knowledge, Skills, and Attitudes Student Learning

4. Specific Learning Goals Number:Use, interpret, and compare numbers in several equivalent forms such as integers, fractions, decimals and percents. Algebra: Symbolic equations can be used to summarize how the quantity of something changes over time or in response to other changes. Data: Comparison of data from two groups should involve comparing both their middles and the spread around them.

5. Examples of Instructional Criteria Represents ideas effectively:Does the material/teaching use accurate and comprehensible representations of the ideas in the learning goals? Encourages students to explain their ideas: Does the material/teaching provide opportunities for each student to express, clarify, justify, and represent their ideas relevant to the learning goals? Guides student interpretation and reasoning: Does the material/teaching guide student interpretation and reasoning about activities and ideas?

6. Fidelity Fidelity is defined by the extent of alignment to specific learning goals and to research-based instructional criteria.

8. Advantages of this Definition • Allows us to look at teaching of key mathematics ideas across several curriculum materials • Maximizes our sample size • Acknowledges diverse ways to achieve high quality practice (rather than following a script) • Encourages teachers to be “better” than curriculum materials

9. Challenges of this Definition • Requires precise clarification of what it means to “meet” indicators of each of the criteria (across various enactments of 4 different curriculum materials and 3 different learning goals) • Requires clarification of what constitutes a “sighting”

10. Does Heisenberg Principle Apply? Perhaps, but less likely, given • Teachers taped for several lessons over three years • Teachers analyzed their own videos during professional development

11. A Case of Change • Veteran 6th grade mathematics teacher • Experienced using highly rated mathematics curriculum material • Participated in both videotaping and professional development for three years • Rural-suburban school

12. Something’s Different in Year 3 Years 1 and 2 Year 3 Making a Leap

13. How Well Does Teaching Encourage Students to Explain their Ideas? • Indicator 1. The teaching encourages students to express their ideas relevant to the learning goals. • Indicator 2. The teaching encourages students not only to express but also to clarify, justify, interpret and/or represent their ideas. • Indicator 3. The teaching provides opportunities for each student (rather than just some students) to clarify, justify, interpret and/or represent their ideas. • Indicator 4. The teaching provides students with feedback about their ideas, either from the teacher or other students, or from follow-up in the textbook.

14. Encourages Students to Explain Their Ideas Year 1 Year 2 Year 3

15. Current Status of the Study • Data collection nearly complete • Classroom videotapes of 3-5 lessons over 3 years for each learning goal • Student assessments (pre and post instruction) on each learning goal • Background data on students • Scoring of student assessments nearly complete • Analysis of videotapes underway • Examination of relationship between teaching and learning awaits completion of video analysis

17. Classroom Observation Instrument ...and then analyzed using a custom online utility developed by Project 2061.

18. Identifying Points

19. Number Line, Grid Area, & Partition Models