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ETL123: Mathematics

ETL123: Mathematics. 3: Planning Problem-Based Lessons Van De Walle Ch 3 and 4. Problem-Based Activities. Used for teaching Concepts (fractions greater than 1) Processes (2 digit addition) Good Problems Begin where the students are Have Maths as the centre of the problem

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ETL123: Mathematics

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  1. ETL123: Mathematics 3: Planning Problem-Based Lessons Van De Walle Ch 3 and 4

  2. Problem-Based Activities Used for teaching • Concepts (fractions greater than 1) • Processes (2 digit addition) Good Problems • Begin where the students are • Have Maths as the centre of the problem • Require reasons for methods of solution

  3. Making Problem-based Activities • Determine Maths outcome/objectives e.g.? • Ensure it has multiple entry points (approaches/strategies/hints) Check by trying it yourself • Create meaningful/engaging contexts (stories, news, links to other KLAs) e.g.?

  4. Teach Students Problem-Solving Steps See also DoL Dim 4 (Marzano 1997: 205)

  5. Teach/Remind Students of Multiple Entry Points or Strategies • Draw a picture/use a model • Look for a pattern • Guess and check • Make a table or chart • Try a simpler form of the problem • Make an organised list • Write an equation

  6. Student Talk and Telling If a student’s stuck . . . When a student’s finished . . . Ask: How did you solve it? Why that way? Why d’you think the answer makes sense? Show/tell me how you did it Tell: Maths conventions for symbols and names (after concept understood), alternative methods (more efficient), clarification of student methods/related ideas What are you thinking? How can I help you?

  7. Evaluating your Activity Check: • How it’s done (do it yourself, check resources / misconceptions) • Purpose (outcomes/goals, skills, links) • If activity achieves purpose • How you’ll write up 3-phase lesson plan

  8. 3-phase Lesson: BDANot 2-phase: explain then drill • Before: activate prior knowledge, ensure problem is understood, establish clear expectations • During: Let go, listen actively (active listening: Communication strategies), give hints, give good extension activities • After: help students listen to each other, listen actively, summarise main ideas, identify future problems

  9. Planning the Lesson: link to LMQs • Maths Goal/objectives: observable/measurable • Student Needs: prior knowledge; vocab/visual support; misconceptions • Select/Design Task: from VDW, CMIT, DENS, DoL to meet 1 and 2 • Design Assessment: profiling/formative/summative; link to goals • Plan Before activities: prior knowl, engaegment • Plan During activities: hints, extensions, questions • Plan After discussion: how begin? How record student ideas? • Check Alignment of objectives, assessment, questions • Anticipate Student Approaches misconceptions? Address in Before • Identify Essential questions that meet objectives of BDA phases

  10. Variations • 3-phase lesson could be over several days • 3-phase lesson could be a 10 min activity • Use stations (rotations): one for each 3-phase lesson (some could be the same) explain task at start have instructions at stations task/game might not be problem solving, but needs to encourage reflection and recording

  11. Planning for All Learners • Accommodations (don’t modify task but presentation) • Modifications (modify task) • Differentiating Instruction (degree of assistance given, amount of scaffolding, number of instructions given at once • Mixed ability groups: individual accountability, shared responsibility • ESL learners: extra 10-step planning questions . . .

  12. Planning for ESL learners • Establish language objectives • Consider cultural background; prev learned vocab • Make context relevant; eliminate vocab not needed • If student not succeeding, work out ways to determine of problem is with language, maths or both • Link task to prior knowledge/contexts; list key vocab and discuss (Dim2: 54); present task written and verbally; check for understanding • Encourage use of models, pictures; maximise English language - use sentence starters to scaffold; think-pair-share • Encourage use of visuals; give advance notice of talking requirement; give ‘wait time’ • Check vocab needs are supported; visual support given • Encourage pictures/diagrams to replace words • Translate essential questions; keep English questions clear - short sentences

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