Unit 4: Classroom Strategies and Planning for Mathematical Models
Learning Objectives
At the end of this unit, learners will be able to:
- Analyze exemplar versus non-exemplar use of mathematical models
- Analyze exemplar and non-exemplar sequence of questions that can support students’ analysis of the new mathematical model
- Collaborate to create a sequence of questions to support students’ analysis of the new mathematical model
Analyzing the Exemplar versus Non-Exemplar Models
Do:
- Open this document
- Set a timer for 5 minutes. Compare the two works from this document.
- Once the timer is up, record your thoughts on the Jamboard here to the prompt, "Which work should be considered the exemplar? Why and why not?"
Debrief:
- The first work is NOT considered the exemplar because the information is not organized in the correct order. This is because there was no labeling in the ratio table(computer, calculator, or total). This model also did not answer the question
- The second work is NOT considered the exemplar because there is no labeling in the ratio table. Even though the answer was correct, there was also no concluding sentence to answer the questions. This raises a question of whether this student knew what they were doing or just simply put the number in the right column
- The third work is considered THE EXEMPLAR because there was labeling in each column of the ratio table. The numbers were organized in the correct column. There was also a concluding sentence that explains the answers within the model, showing conceptual understanding of the problem, skill and model.
- Think: What are some criteria of success of an exemplar use of model?
Mini-Stamp:
A mathematical model has to be used correctly in order to get the right answer. A strong mathematical model includes the uses of labeling, matching number sentence, and alignment to the problem itself. The model does not replace the process of solving itself, but can be used as a tool to solve it. This will help the students to understand what is going on in the problem and solve the problem correctly.
Analyzing the Exemplar versus Non-Exemplar Questioning
Do:
- Open the document below
- Set a timer for 5 minutes. Compare the two sequences of questions from the same problem you just worked with
- Once the timer is up, record your thoughts on the Jamboard here to the prompt, "Which sequence of questions is considered exemplar and can best support correct use of mathematical models? Why or why not?"
Debrief:
- The first sequence of questions is NOT considered the exemplar because the questions are too open-ended and not targeted towards the use of the model. Students who struggle with the model might be confused and not able to catch up with the work because the questions are too broad. There is no emphasis on the habit of modelling (labelling and organization). Last but not least, this sequence of questions did not
- The second sequence of questions is considered the exemplar because the teacher plans the expected answers from the students, which is used to build the next questions. There is an emphasis on targeted parts of the model (where the second set of ratios come from or how to find missing computers. This sequence of questions is also an exemplar because it puts heavy emphasis on good habits of modelling such as labelling, organization, and concluding sentences. Students who struggle can understand how this work is correct and can be used to solve the problem because the questions go from open-ended to close-ended.
- Think: What are some criteria of success of an exemplar sequence of questions that can support the correct use of models and mastery of new concepts?
Mini-Stamp:
An exemplar sequence of questions that can support the correct use of models involve the following criteria:
- Show-calling exemplar students work
- Ask open-ended questions to close-ended questions
- Targeted misconceptions and errors to support successful use of models
- Possible use of error analysis with targeted questioning
- Questions lead to the lesson's key points and are directly aligned to the objective
Practice: Group Work
Together with your assigned group, create the exemplar sequence of questions to the non-exemplar one you just worked with. As you work collaboratively, use the criteria of success for an exemplar sequence of questions.
Once you are done, send the exemplar questions in a pdf file to my email at emily.duong@albany.edu
Self-Reflection
Reflect: Set a timer for four minutes and write down some key takeaways from today's unit. As you reflect, use the following guiding questions:
- What stood out to you about this unit?
- How did this unit align/contrast/add to your practice and/or belief?
Unit Takeaways
STAMP
A mathematical model has to be used correctly in order to get the right answer. A strong mathematical model includes the uses of labeling, matching number sentence, and alignment to the problem itself. This will help the students to understand what is going on in the problem and solve the problem correctly.
An exemplar sequence of questions that can support the correct use of models involve the following criteria:
- Show-calling exemplar students work
- Ask open-ended questions to close-ended questions
- Targeted misconceptions and errors to support successful use of models
- Possible use of error analysis with targeted questioning
- Questions lead to the lesson's key points and are directly aligned to the objective