Session 1: Explore the Inquiry Topic & Reflect on Your Current Practice

Outside-of-class meeting | Time: 1 hour | Materials: Class set of recent student journals

Focus

In this session, you will examine journals to see how students draw on their prior knowledge, consider strategies to encourage this habit and identify strategies to try in your classroom.

The field of mathematics grows because mathematicians use prior knowledge to build new concepts and procedures. How can we help our students build this key mathematical disposition?

“Tasks must allow students to treat the situation as problematic, as something they need to think about rather than a prescription they need to follow. …In order for students to work seriously on a task, it must offer students the chance to use skills and knowledge they already possess” (Hiebert, Carpenter, et al. 1997, p. 18).

Help students become aware of the role their ideas and prior knowledge play.  For example, teacher Bill Jackson uses a thought bubble on the board

• Encourage students to look back at in their journals, by asking questions such as “What do we already know that might help us solve the problem?”or , “Where can we look to help us remember what we have already done?” When students use their journals as a reference, bring this to the attention of the class.

1A: Reflect on Your Current Practice

• What were some successes you had in using the new strategies to encourage students’ use of prior knowledge?
• What were some challenges?
• What aspects of these strategies would you like to carry forward into your future instruction?
• What would you like to change or add?

1B: Learn about New Strategies

Colleagues and research can be great sources of additional ideas for building a classroom environment in which students routinely draw on their prior learning.  Here are several that were shared with us. Try these or brainstorm your own.

• When you pose a new type of problem to students, ask them what they notice about it or what they already know that might help them solve it.  You can see an example of this in the classroom here:

Confronted for the first time with a problem of adding fractions with unlike denominators, students noticed that the denominators differed and that it was addition (not comparison) of fractions, sparking the two key pieces of prior knowledge that would enable the students to develop (rather than be given) an addition procedure–their knowledge of fractions addition and equivalence.

• Help students become aware of the role their ideas and prior knowledge play.  For example, teacher Bill Jackson uses a thought bubble on the board to highlight ideas that students come up with as they think about a novel problem. Students may enjoy using bubbles or other symbols to note their questions and their ideas about related knowledge.
• Encourage students to look back at in their journals, by asking questions such as “What do we already know that might help us solve the problem?”, “Where can we look to help us remember what we have already done?” When students use their journals as a reference, bring this to the attention of the class.

1C: Plan to Try New Strategies

• Identify one or two strategies you will try in your classroom, designed to build students’ use of prior knowledge
• Identify evidence will you look for in journals to inform you about the impact of the strategies

Session 2: Try New Strategies in Your Classroom

In class | Time: 3-5 lessons over 1 to 2 weeks

• Try out the strategies in your plan for approximately 3-5 lessons in which journals are being used
• If possible, jot down notes during or soon after each lesson to capture your experiences with the strategies that you tried
• Bring your notes and the class set of students’ journals to the next session

Session 3: Examine Evidence and Refine Your Plan

Outside-of-class meeting | Time: 30-60 minutes

3A: Examine Evidence from Lessons and Revise Plan

• What were some successes you had in using the new strategies to encourage students’ use of prior knowledge
• What were some challenges?
• What aspects of these strategies would you like to carry forward into your future instruction?
• What would you like to change or add?

3B: Make a Plan for Your Second Round

• Identify a new strategy (and/or a refined strategy) you will try in the upcoming 3-5 lessons to encourage students’ use of prior knowledge
• Identify the evidence will you look for to inform you about the impact of this change

Session 4: Test Your Refined Approach

In class | Time: 3-5 lessons over 1 to 2 weeks

• Try out the strategies for approximately 3-5 lessons in which journals are being used (about 1-2 weeks)
• If possible, jot down notes during or soon after each lesson to capture your experiences with the strategies that you tried
• Bring your notes and your students’ journals to the next session

Session 5: Examine Evidence and Reflect on this Inquiry Cycle

Outside-of-class meeting | Time: 30-60 minutes

5A: Examine Evidence and Reflect

Examine students’ journals, focusing on a challenging task(s) where you hoped students would draw on their prior knowledge without explicit instruction to do so.

• What do you notice? For example, what proportion of students drew on prior knowledge? What elements of task design and presentation encouraged (or discouraged) students from bringing prior knowledge to bear?
• For students who did not draw on their prior knowledge, can you imagine experiences that might help them develop this habit?
• What were some successes you had in using the new strategies to encourage students’ use of prior knowledge?
• What were some challenges?
• What aspects of these strategies would you like to carry forward into your future instruction?
• What would you like to change or add?

5B. Reflect on this Inquiry Cycle

• What did you learn that might inform future inquiries–for example, how to collect data, collaborate, find useful resources, etc.
• Is there anything from this inquiry you would like to share more broadly at your school or with the profession?  How will you do this?