TEACHING MATHEMATICS Through Problem Solving Amelia Buan Grace Liwanag Joan Rose Luib

The K - 12 Mathematics Curriculum

The K -12 Mathematics Curriculum Framework

What is a learner-centered lesson? A lesson is learner-centered if it provides the learners plenty of opportunities to engage in higher order thinking skills.

What is a problem? A problem is a mathematically unfamiliar situation that needs a solution but for which the problem solver has no readily available algorithm to use to solve it.

What is problem solving? It is finding a solution to a problem.

Three types of teaching related to problem solving –SCHROEDER (1989) Teaching for problem solving Teaching about problem solving Teaching through problem solving

Teaching for problem solving Problems are given to the students after needed content and skills are taught

Teaching about problem solving Understand the Problem Devise a Plan Carry out the Plan Look Back Problems are given to the students after general method of solving problems and the different strategies are discussed

Teaching through problem solving Problems is given to the students at the start. The problem is used as context to teach the topics as well as to develop skills and apply these skills to unfamiliar situations

What is critical thinking? It is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by observation, experience, reflection, reasoning, or communication, as guide to belief and action.

Experience Observation Critical Thinking Reflection Listening Applying Analyzing Synthesizing Evaluating Experience Observation Reflection Listening

Questioning to Promote Critical Thinking

Prompts for Divergent questions What if…? Suppose that…? How…? Why…? Given what you know about…, why…? What can you conclude from…?

COLLABORATIVE LESSON PLANNING? Learning Objectives Assessments Materials and Activities

Students vary in abilities, interests, attitudes, learning needs Task They approach the same learning task in different ways.

Why do we assess?

Assessment purposes Encourage Collaboration and Self Direction Gauging Student Needs Encourage Collaboration and Self Direction Monitoring Progress Checking Understanding Demonstrating Understanding

TiMSS 2011 Mathematics Framework

TIMSS 2011 Mathematics Framework Reasoning Applying Knowing

knowing recall recognize compute retrieve measure classify Recall definitions Recognize mathematical concepts Carry out algorithmic Retrieve information Use measuring instruments Classify objects/shapes

applying select represent model implement Solve routine problems Select an efficient operation Display mathematical information Generate an appropriate model Implement a set of mathematical instructions Solve standard problems

reasoning analyze generalize integrate justify Solve non-routine problems Use relationships between variables Extend domain to which result of mathematical thinking Make connections Provide justification to known mathematical results Solve problems set in mathematical or real life contexts

Lesson Study

What is a lesson study? Lesson study, a form of collaborative practice, is a school-based professional development initiative that aims to enhance teaching and learning through the methodology of professional sharing of practice (Burghes & Robinson, 2009)

Lesson Study Process L L B O Planning a Research Lesson Implementation of the Research Lesson Post-lesson Reflection & Discussion C O L B R A T I N

Phase One: Presentation of the Problem (10 minutes) Phase Two: Developing a Solution (15 minutes) Phase Three: Progress through discussion ( 10 minutes) Phase Four: Summarizing ( 10 minutes)

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