Presentation on theme: "Problem Solving What’s the problem? Introduce ourselves."— Presentation transcript:
1 Problem SolvingWhat’s the problem?Introduce ourselves
2 “If it can be solved using a procedure or an algorithm, it is not a problem. It’s an exercise.” What is a problem at one time to one child, may be an exercise to another.Ex. Sharing cookies to a student in grade 1 could be a problem but to a child in grade 4…it’s very likely an exercise.What do you think about this quote? Discuss.
3 Why teach through problem solving? The math makes more sense.Provides the teacher with more understanding of the student’s mathematical thinking.A challenge can be very motivatingProblem Solving builds perseverance
4 Builds confidence, maximises the potential for understanding, allows for differences in learning styles and approachesPractice with concepts and skillsProvides students with a stronger understanding of what math is aboutStudents needs to practise problem solving
5 I took a handful of M&Ms. 1/3 of them were red. Draw the handful. BeforeI took a handful of M&Ms. 1/3 of them were red. Draw the handful.DuringYou have ¾ of the pizza left. If you give 1/3 of the left over pizza to your brother. How much of the whole pizza will your brother get?AfterPay attention to how you solved the problem & share your ideas.Taking you through a typical 3-part lesson using problem solving as a focus.
6 What is it?To teach through problem solving, the teacher provides a context or a reason for the learning by beginning the lesson with a problem to be solved and later drawing out any necessary procedures. This approach contrasts with the more traditional approach of presenting a new procedure and only then offering a few problems for students to solve.(P.38 Making Math Meaningful, Marian Small)Simply read. Discuss.
7 Things have changed…. Now Step 1: Begin the lesson with a problem Step 2: Draw out the procedures usedThenStep 1: Teach the procedureStep 2: Provide problems that use that procedure
8 Think about the questions you just worked through. What do you think that lesson would have looked like “then”?
9 A Good Problem: is a question that cannot be answered immediately is challenging to the learnerholds the learners interestmight have several answersmight have 1 answer but many different approachesis often connected to real life
10 3-part Lesson Before Get students mentally ready to work on the task, (Getting Ready)-20 minutesGet students mentally ready to work on the task,Be sure all expectations for products are clear;During(Students Work) – 20 minutesLet go!Listen carefully,Provide hints,Observe and assess;After(Class Discourse) – 20 minutesAccept student solutions without evaluation,Conduct discussion as students justify and evaluate results and methods (reflection).(Adapted from Elementary and MiddleSchool Mathematics:Teaching Developmentally 4th Ed., John Van de Walle)Talk about the lesson that just happened & discuss this though that lens
11 I picked up a handful of M&Ms. One third of them where red I picked up a handful of M&Ms. One third of them where red. What might the drawing of the M&Ms look like?Page 27, #4Examples of resources to find good questions
13 A Problem Solving teacher: Encourages risk takingProvides enough time to studentsRespects and encourages respect for each others thinkingProvides opportunity for discussion and challenge solutionsValues perseverance
14 How to teach problem solving? Begin with the problemTeach students the Three Read StrategyAllow students to work on the problemDraw out the different strategies usedThree-read strategy1st Read→Visualise→ set the context→ get a general impression2nd Read→ listen for details→ gather the facts→ determine what question is being asked3rd Read→Check the facts→ check the understanding of the questionSolve!
15 → gather the facts and decide what you’re being asked to find Three-read strategy1st Read→Visualise the context(ask students general questions)2nd Read→ gather the facts and decide what you’re being asked to find-3rd Read→verify your facts, clarify what you have to find.Solve!1st Read General Questions: about pizza & fractions & brothers2nd Read: ask students to records these things; when hands shoot up glace at their paper & see if they’ve done this first…nothing get answer til then
19 FERMI QuestionsEx. How many piano tuners are there in Toronto?People crowd into London until all available open space within the city limits is covered with standing people. How many people would there be?How many hairs are there on a human head?
20 Some problem solving resources Making Math Meaningful Marian SmallRoads to ReasoningPuddle QuestionsNCTM websiteMath Makes Sense texts
21 Taken from Puddle Questions Grade 3 Joan Westley