Presentation on theme: "Big Ideas and Problem Solving in Junior Math Instruction"— Presentation transcript:
1 Big Ideas and Problem Solving in Junior Math Instruction
2 What is it all about? Mathematics is a fundamental human activity a way of making sense of the world.Children possess a natural curiosity aninterest in mathematics, and come to schoolwith an understanding of mathematicalconcepts and problem-solving strategies thatthey have discovered through explorations ofthe world around them (Ginsburg, 2002).
3 What is a big idea in mathematics? “Students are better able to see theconnections in mathematics and thus to learnmathematics when it is organized in big,coherent “chunks”. In organizing amathematics program, teachers shouldconcentrate on the big ideas in mathematicsand view the expectation in the curriculumpolicy documents for grade 4-6 as beingclustered around these big ideas.”p.12
4 For us as teachers… The big ideas also act as a lens for: Making instructional decisions (e.g., deciding on an emphasis for a lesson or a set of lessons)Identifying prior learningLooking at students’ thinking and understanding in relation to the mathematical concepts addressed in the curriculum (e.g., making note of the strategies a student uses to count a set or to organize all possible combinations to solve a problem)Collecting observations and making anecdotal recordsProviding feedback to studentsDetermining next stepsCommunicating concepts and providing feedback on students’ achievement to parents (e.g., in report card comments)p.34
5 Problem Solving An information- and technology-based society requires individuals who are able to thinkcritically about complex issues, people who can“analyze and think logically about newsituations, devise unspecified solutionprocedures, and communicate their solutionclearly and convincingly to others” (Baroody,1998, p. 2-1me_2.pdf p.3
6 As students engage in problem solving, they participate in a wide variety of cognitive they will encounter throughout their livesThey:Learn mathematical concepts with understanding and practice skills in contextReason mathematically by exploring mathematical ideas, making conjectures, and justifying results;Reflect on and monitor their own thought processesSelect appropriate tools (e.g., manipulatives, calculators, computers, communication technology) and computational strategiesConnect the mathematics they learn at school with its application in their everyday livesDevelop strategies that can be applied to new situationsRepresent mathematical ideas and model situations, using concrete materials, pictures, diagrams, graphs, tables, numbers, words, and symbolsPersevere in tackling new challenges;Formulate and test their own explanationsCommunicate their explanations and listen to the explanations of othersParticipate in open-ended experiences that have a clear goal but a variety of solution pathsCollaborate with others to develop new strategies.p.4-5
7 4 Steps to Problem Solving In the words of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario, 2004 p.9, “instruction based on a problem- solving or investigative approach is the means by which Ontario students will most readily achieve mathematical literacy”
8 Classroom Structures That Support Problem Solving: A big idea, problem solving math teacher:Chooses problems that offers a range of entry points for students at different levels. Every classroom contains students with a range of understandings and prior knowledge. Teachers need to choose problems that can beaccessed in some way by the studentsEngages the interests of students by using problems that are culturally, socially, etc. relevantUses a variety of mathematics instruction - guided, shared, and independentPlans and integrates a variety of groupings to provide students with time to share ideas with their peers and to work independentlyEncourages oral communication is essential for learning math to help students clarify their ideas, get feedback for their thinking, and hear other points of view. Students learn from one another as well as from their teachersHas students communicate and investigate their thinking throughongoing discussionAllows students to make sense of the problem in their own way. To look for patterns and for connections with other problems. Different methods of solving problems are welcomed and shared
9 Classroom Structures That Support Problem Solving (cont’d) A big idea, problem solving math teacher:Presents math activities in real world contexts to give students access to otherwise abstract mathematical ideasSupports math learning with manipulatives, to make abstract mathematical ideas concrete.Engages student interest in mathematical ideas, even when they are not related to the curriculumIncludes students as active rather than passive participants in their learning;Encourages confusion and mistakes as opportunitiesfor learning;Has students explain their thinking, to help organize their ideas and extend their understanding.Encourages writing in math class, so students revisit their thinking and reflect on their ideas.Incorporates ongoing assessment of student understanding to guidefuture instruction.Wants the acquisition of mathematical knowledgeby all students a top priority
10 Importance of Communication in Problem Solving Junior students are developing their ability to communicate their thinking to others orally and on paperStudents need to talk about the problem to understand it better. Students discuss ideas with others to clarify which strategy or strategies would work bestStudents trying to engage and answer questions from teachers and peers in proper mathematical language e.g. “I then divided the number of marbles” makes the terminology realStudents teaching their peers aloud, effectively communicates and solidifies what they have learnedAs important as effective communication is active listening in which students listen to the ideas and learning of a partner, group members and/or the teacher teachers is just as important in helping them develop the understanding and metacognition.
11 Resources and Strategies to Help Further Develop Your Understanding Teaching and Learning Mathematics: The Report of the ExpertPanel in Grades 4-6 Math. in Ontariohttp://eworkshop.on.ca/edu/resources/guides/ExpPanel_456_Numeracy. pdfBig ideas in math eworkshopsBig ideas in number sense and numeration gr.4-610 big math ideas 10-big-math-ideasA guide to effective instruction in math, kindergarten – grade 60K-6/GEIM%20K-6.pdf