Problem-Based Lesson Implementation & Analysis
Problem-Based Lesson Implementation & Analysis
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We adjusted a lesson from the curriculum that is engaging and deepens students' mathematical understanding. We anticipated student strategies, developed a discourse plan, and taught the lesson. After our lesson, we analyzed student understanding, planned the next instructional steps, and reflected on our experience.
We adjusted a lesson from the curriculum that is engaging and deepens students' mathematical understanding. We anticipated student strategies, developed a discourse plan, and taught the lesson. After our lesson, we analyzed student understanding, planned the next instructional steps, and reflected on our experience.
The Problem-Based Lesson Implementation & Analysis allowed us the opportunity to adapt a mathematics task to support a learning goal that students had been working on for several weeks, (II.b.i). Prior to teaching the lesson, we looked over what vocabulary would need to be introduced and provided sentence frames to support students in discussing their math ideas, processes and solutions, (II.b.ii). We also anticipated student solutions and representations and how they connect to one another, (II.b.iii), and preemptively developed questions to ask students to assess and advance student thinking, (II..b.iv).
This year I am an instructional specialist and although I know each of the students and how they perform in their academics, I do not have my own homeroom of students. I went into a colleagues third grade classroom to implement this lesson. I knew this teacher has used the curriculum daily and this task would have utilized and built upon learner's existing knowledge, (II.a.i). Using my own background knowledge of the students in this class, I felt like I could provide scaffolds and motivation as needed but I also wanted students to sit in that productive struggle for awhile, (II.a.ii, II.a.iii, II.b.vx). I had students work independently and then allowed them to work in partners or small groups, (II.b.vix), to allow engagement between partners to share different representations, discuss their mathematical explorations, and further their learning (II.ai.v). Once in the middle of the lesson and again when our time together was almost over, I allowed a few students to share their work with the class. They communicated their solutions as well as the process they took to get there, (II.b.v). I helped guide students in the direction of making connections between the various representations that students' used and I asked questions to about why students did things in a particular way, but I feel like an area of weakness in this lesson was "modeling effective problem solving and mathematical practices", (II.b.vi). I usually feel like this is a strength of mine and I wonder if I did not do this well because this task was more of a culmination of everything students had learned over the unit. I do believe many students performed well with various mathematical practices, but I did not model such because I wanted to see what students knew.
After the lesson, I analyzed the students' work more closely to examine representations, determine misconceptions, evaluate solutions, and planned next steps to further student understanding, (II.b.viii). I also reflected on my teaching, interactions, responses, and determined next steps to better my instruction. Overall, this entire project was such a great experience and I really hope that I can replicate this with my colleagues. I wonder if it could be a coaching cycle that people opt into. As teachers we often run out of time to really plan lessons, analyze student work with a fine tooth comb, and reflect on our teaching all while planning next steps. Even if I could support teachers to do this a few times a year, I think it would be such a great opportunity for educators and their students.
See how a couple of of third graders examined and solved the problem below. Students were given an engaging real world problem to solve. A neighborhood pizzeria was opening up and Chef Itsa needed some help with the menu.
Mathematics Specialist Standards
Mathematics Specialist Standards
Content Standards:
3.NF.A.1: Understand a fraction 1/ b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a / b as the quantity formed by a parts of size 1/ b .
3.NF.A.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
3.NF.A.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
3.NF.A.3b: Recognize and generate simple equivalent fractions, e.g., 1/2=2/4, 4/6=2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Pedagogy Standards, from AMTE, 2013:
Learners and Learning. Mathematics Specialist professionals must know and be able to:
II.a.i. Utilize and build upon learners’ existing knowledge, skills, understandings, conceptions and misconceptions to advance learning.
II.a.ii. Understand learning trajectories related to particular topics in mathematics (e.g., Common Core Standards Writing Team, 2013; Maloney & Confrey, 2013; Sarama & Clements, 2009) and use this knowledge to organize and deliver instruction that is developmentally appropriate and responsive to individual learners.
II.a.iii. Understand cultural differences among learners (e.g., algorithms or learning practices familiar to different groups of learners) and utilize this knowledge to motivate and extend learning opportunities for individuals and groups of learners.
II.ai.v. Create social learning contexts that engage learners in discussions and mathematical explorations among peers to motivate and extend learning opportunities.
Teaching. Mathematics Specialist professionals must know and be able to:
II.b.i. Design, select and/or adapt worthwhile mathematics tasks and sequences of examples that support a particular learning goal.
II.b.ii. Support students’ learning of appropriate technical language associated with mathematics, attending to both mathematical integrity and usability by learners.
II.b.iii. Construct and evaluate multiple representations of mathematical ideas or processes, establish correspondences between representations, and understand the purpose and value of doing so.
II.b.iv. Use questions to effectively probe mathematical understanding and make productive use of responses.
II.b.v. Develop learners' abilities to give clear and coherent public mathematical communications in a classroom setting.
II.b.vi. Model effective problem solving and mathematical practices—questioning, representing, communicating, conjecturing, making connections, reasoning and proving, self-monitoring—and cultivate the development of such practices in learners.
II.b.viii. Analyze and evaluate student ideas and work, and design appropriate responses.
II.b.vix. Develop skillful and flexible use of different instructional formats—whole group, small group, partner, and individual—in support of learning goals.
II.b.vx. Manage diversities of the classroom and school—cultural, disability, linguistic, gender, socio- economic, developmental—and use appropriate strategies to support mathematical learning of all students.
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