Eight Grade 2 mathematics teachers of a public elementary school in Quezon City together with the Elementary School Mathematics group of UP NISMED collaboratively developed a research lesson on solving problems involving multiplication of whole numbers under the project Collaborative Lesson Research and Development (CLRD) of the Institute. In planning the lesson, the teachers agreed to deviate from using the AGONA (What is **A**sked?, What are **G**iven?, What **O**peration will be used?, What is the Number sentence?, and What is the **A**nswer?) in analyzing and solving problems and to encourage pupils to present different ways of solving a problem. Read the rest of this entry »

# Category Archives: Mathematics

## Classroom Problem Solving Practices Involving Multiplication of Whole Numbers

## Beyond Collaboration: An Appreciative Inquiry Into Lesson Study

This study uses *appreciative inquiry* into lesson study in which the overall design is governed by qualitative inquiry focus on: (a) stories and images that helped teachers in doing lesson study in a new and constructive light; and (b) qualities of lesson study would help make it sustainable. Appreciative inquiry is adopted as a method based on the assumption that researches which apply this are participative in nature and recognizes that teachers learn collaboratively by adapting their knowledge to their experiences. Read the rest of this entry »

## An Analysis of Problem Solving Activity in a Mathematics II Class

In the project Collaborative Lesson Research Development (CLRD), four Mathematics II teachers together with a UPNISMED facilitator collaboratively developed, critiqued, and revised a lesson on Solving Quadratic Equation Using Quadratic Formula. The lesson utilized the approach teaching * **through** *problem solving. Teaching* **through* problem solving is an approach wherein a problem is given to the students at the start and is used as context to teach a topic as well as to develop skills and apply these skills to unfamiliar situations. It is characterized by students’ deep construction and understanding of mathematical ideas and concepts. The problem in the lesson used a real life context and it involved different ways to solve it. The nature of the problem provided an opportunity for the students to apply their previous knowledge and skills and experience thinking skills like representing, looking for patterns, and generalizing.

The study focused on the content of the problem solving activity of the lesson. How the students progressed in the problem solving process and how the teacher provided scaffolding so that the students would complete the task were the ones given particular attention. To follow up the students’ progress and the scaffolding the teacher provided during the problem solving activity, Polya’s Four Steps of Solving a Problem was used as a guide. At first, the students experienced difficulty in solving the problem. However the difficulty was addressed when the teacher provided the necessary scaffolding.

The result of the problem solving activity was an “eye opener” to the four Mathematics II teachers. They realized that the reason why the students had difficulty in solving the problem was that they were not exposing the students to problems involving multiple solutions; to problems involving the skills of looking for a pattern, generalizing and “modelling”. The problems they usually give are problems involving only one solution and an answer of numerical in nature.

The full text of the study is one of the chapters of the book titled “BOOK 1. LESSON STUDY: PLANNING TOGETHER, LEARNING TOGETHER” which will be published in print form by UP NISMED this first quarter of 2013.

## Research Lesson on Geometric Relations

The Mathematics III Lesson Study Group of Santa Lucia High School which was composed of four mathematics teachers and one UP NISMED facilitator highlighted multiple solutions in their research lesson on Geometric Relations. The lesson was about the Parallel Postulate which was an offshoot of the problem shown below. In the problem, if a horizontal diagonal is drawn, the diagonal and the line segment containing the base are parallel and the two sides that connect the parallel segments are transversals. This leads to the concept that corresponding angles are congruent which is known as the Parallel Postulate.

During lesson planning, the teachers and the facilitator came up with 11 anticipated solutions. Questions were formulated on how to process the solutions. Follow up questions were listed in case students could not answer the questions. The key questions and the expected answers were emphasized in the lesson plan.

The lesson was implemented for two days in four sections. Most of the students used previous knowledge in solving the problem, but there were some who came up with intuitive solutions. Some solutions presented were not even anticipated by the teachers and the UP NISMED facilitator.

After each lesson implementation, the facilitator and the teachers met to discuss what went well, what went wrong, and the strategies to be used to improve the lesson.

The teachers were pleased with the result of the thorough planning. They were able to anticipate students’ answers and were able to address misconceptions. They also observed that students were more participative and active in class discussions.

## Math Lesson Study Groups

To date, UP NISMED has facilitated lesson study groups in several public high schools within the Metro Manila area. The first model of lesson study implementation was in 2006 and the second model, a refinement of the first, was conducted in 2010.

Batch 2007 was attended by teachers from Rizal High School in Pasig, Balara High School in Quezon City, San Vicente Elementary School and Krus na Ligas Elementary School, both in Quezon City. From these, a total of six high school lesson study groups and ___ elementary lesson study groups conducted lesson study in varying degrees.

For its second batch of lesson study, NISMED concentrated in one school in Pasig – Sta Lucia High School. As in Rizal High School, one lesson study group was organized for each year level involving all the teachers in the year level.

In 2011, NISMED conducted its first lesson study in a school outside Metro Manila with the teachers of Ligao National High School (LNHS). Lesson study was also introduced to the math and science teachers of Nueva Ecija High School last February 2012.

ES Math Lesson Study Topics