89 Introduction to Understanding Problems in Math

Introduction to Understanding Problems in Math What is Involved in Understanding Problems • • • • • Rereading the problem Annotating words and numbers Visualizing the situation Converting visualizations into diagrams or mathematical expressions Assessing the reasonableness solutions Key Elements of Understanding a problem • Learning how to solve word problems requires students to: – understand the context – develop a strategy to solve the problem – build upon their ability to organize, create visual representations, and use precise language How Does Understanding Problems Help Students? • Helps students – make sense of problems – see that a problem is not just a jumble of words and numbers – deal with increasingly complex situations as they move forward in their mathematical learning Discussion Questions 1 Is there a systematic problem solving process you use? What strategies (e.g., thinking aloud, organizing, modeling, visual representations, precise language, and/or peer interaction) your students employ? What aspects of problem solving your students struggle with? How Can I Support Student Use of Understanding Problems? Use of Evidence-Based Practices • • • Provide Clear Explanations Give Students Strategies and Models Provide Ongoing Formative Assessment Differentiated Instruction • • Plan instruction that considers students' readiness, learning needs, and interests Use a range of technology tools to: – engage learners at varying levels – engage learners in multiple ways – offer students options for demonstrating understanding and mastery Teacher-Dependent Ways to Differentiate • By Content – Different levels of reading or resource materials, reading buddies, small group instruction, curriculum compacting, multilevel computer programs and Web Quests, audio materials, etc • By Process – Activity choice boards, tiered activities, multi-level learning center tasks, similar readiness groups, choice in group work, varied journal prompts, mixed readiness groups with targeted roles for students, etc • By Products – Tiered products, students choose mode of presentation to demonstrate learning, independent study, varied rubrics, mentorships, interest-based investigations Student-Dependent Ways to Differentiate • By Readiness – Options in content, topic, or theme, options in the tools needed for production, options in methods for engagement • By Profile – Consideration of gender, culture, learning styles, strengths, and weaknesses • By Process – Identification of background knowledge/gaps in learning, vary amount of direct instruction, and practice, pace of instruction, complexity of activities, and exploration of a topic Discussion Questions How can you use CCSS Mathematical Practices and the UDL principles to enhance student comprehension in the problem solving process? How you build differentiation into teaching students to understand problems? How have you used technology to differentiate instruction? Provide Clear Explanations: Possible Strategies • Use prompting questions and give students sufficient time to understand and react – Ask students to present the directions or explanations in their own words – Ask students to compare and contrast different approaches Use Varied Examples, Materials, and Models: Possible Strategies • Use a process chart to guide students • • Create a “gallery walk” to expand their repertoire of appropriate models Show students how to embrace mistakes and errors as part of learning • Provide Ongoing Formative Assessment: Possible Strategies Ask students to explain – what they are doing – their use of pictures, diagrams, charts, expressions, and equations – if their process makes sense to them Use Online and Offline Tools • Manipulatives • Interactive whiteboard • Web-based applets • Math drawing tools • Calculators • 3D design software • Graphing and charting software Use Research-Based Strategies and Tools • • • To launch the lesson During the learning task As you bring closure to the lesson Discussion Questions What are some methods you have used to effectively expand students’ understanding of different solution methods? How you teach students to compare and contrast different approaches to solving a problem? What technology tools have you used to support formative assessment? 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