Algebraic Reasoning Inquiry Project Monday July 7, 2014

Algebraic Reasoning Inquiry Project Purpose: Identify and develop an inquiry into your students’ algebraic reasoning that you will implement during the school year. Paper: Due August 15 Presentation: Due Aug 12 or 13

Sample Topics Understanding of equality and the equals sign Subitizing Develop relational thinking Mental math strategies based on properties of the operations (single-digit or multi-digit numbers) Meanings of the operations (e.g., subtraction) Representational competence for multiplication Subitizing Anchors of five and ten Tape diagrams to represent and solve word problems. Multi-step word problems And so on . . .

The Process Identify a topic. Read more about that topic. Narrow the topic to the “slice” you will study. Formulate 1-3 “action” research questions to investigate. Design a pre/post “critical point diagnostic assessment” that will give you data to answer your research questions. Develop an instructional guide to support your ongoing work with students. 1. My students’ understanding of multiplication. 2. From my reading I learned that students have misconceptions about multiplication in that they think the answer is always bigger (citation), that students might be able to do the procedure or memorize their facts but it is not connected to problem situations (citation), and that students often can not pose their own multiplication problems (citation). 3. My slice: Representational competence related to the meaning of multiplication. 4. Questions: Are my students able to alternate directionality among the representations (e.g,, go from Symbols to RW context; go from symbols to equations)? Can my students represent multiplication situations using a variety of visual representations---equal groups, arrays, tape diagrams, and number lines? 5. Pre/Post: My standard, define mult, explain, draw a picture, write a story. Then represent the following word problem with 3 different visual representations. Instructional Guide: Things that I will emphasize in my instruction, might be .....

Critical Point Diagnostic Assessment Find or develop a few “power questions” that will reveal your students’ understanding on a specific slice of your topic. (Yes, 4 items is enough.) Must include a request for students to explain and justify their reasoning in writing or to state it orally. Based on what your analysis, you might need to adjust or add items on the post-assessment. You decide on the time frame (e.g., 1 month, 3 months), just pick a spot to post-assess and identify learning to that point in time and further needs.

Example: Multiplication Understanding Solve 4 x 6 = o Explain how you solved it. Draw a picture of 4 x 6 = o. Write a story problem for 4 x 6 = o.

Example: Fraction Screener

Instructional Guide “Guide” or general plan. Benchmarks of student reasoning that you are working to develop over time. If helpful, include key questions, sample tasks, and check-in prompts.

Paper: Due Aug 15 Identification of topic of problem being studied Literature review (at least 10 sources, more if doing a collaborative project with another individual) Research questions (or “wonderings”) Procedures and Instruments (CPDA) for data collection Procedures/guide for instruction Anticipated results in regards to student proficiency Reference List

Presentation: Aug 12 or 13 5-10 minutes (present and engage) PowerPoint slides or something similar. Summarize 1-3 key ideas from the literature. Engage us in thinking with you about your project: Administer one of your assessment items to us. Solicit feedback on your assessment or on your instructional ideas to support student learning.

Presentation Template “Suggestion” Title Problem/Purpose Literature Review Insights Share 1-3 important ideas with citations. Assessment Items Discuss what you are going to ask and why. Anticipated Results (some closing slide)

Tonight: Ponder further what you might want to study and why. Discuss and raise questions in class on Tuesday.

Algebraic Reasoning Inquiry Project Tuesday July 8, 2014

Algebraic Reasoning Inquiry Project Purpose: Identify and develop an inquiry into a “slice” of your students’ algebraic reasoning that you will implement during the school year.

What topic am I considering as the focus of my inquiry project? Take turns: My broad topic is ... The slice I might focus on is... Help me think about ... Perhaps time the discussion so each person has about 3 minutes or just let them talk.

What am I understanding as the process to follow for the project? Person 1: We need to.... Person 2: Add on an important part of the process. Person 3: Add on another point. Person 4: Add on another point. Then discuss, as a group, your initial understanding of the expectations and the process. Perhaps time the discussion so each person has about 3 minutes or just let them talk.

Paper answers.... What problem of practice (topic) are you studying? What did you learn from a brief literature review that is informing your inquiry? What specific “questions” or “wonderings” are you investigating? How will you collect information (data) to address your questions (i.e., assessment items, procedures)? What might be a general plan for instruction (e.g., benchmarks of student reasoning, key questions, sample tasks, and time frame)? What are my anticipated student results for this time frame (i.e., I’m hoping that my students will make progress in....)? Reference List

Algebraic Reasoning Inquiry Project Wednesday July 9, 2014

What am I understanding as the process to follow for the project? Person 1: We need to.... Person 2: Add on an important part of the process. Person 3: Add on another point. Person 4: Add on another point. Then discuss, as a group, your initial understanding of the expectations and the process. Perhaps time the discussion so each person has about 3 minutes or just let them talk.

Disclaimer Pathways to Teacher Leadership in Mathematics Project University of Wisconsin-Milwaukee, 2014-2017   This material was developed for the Pathways to Teacher Leadership in Mathematics project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II Improving Teacher Quality Program.