If you know where you are going, it doesn’t always follow that you also know how to get there. Understanding by Design (UbD) supports the first part of the statement: knowing where you are going. Its three-stage curriculum planning framework is useful as a general guide for identifying where to lead the students in terms of understanding what they are supposed to be learning.
In Stage 1: Desired Results, teachers think about what goals they would like their students to learn. They also jot down the “big ideas”, “essential questions”, and what students should know after the lesson.
From 2006 – 2009, the University of the Philippines National Institute for Science and Mathematics Education Development (UPNISMED) piloted a school-based professional development program for teachers called Lesson Study to two high schools and two elementary schools in Metro Manila. The project involved all the mathematics teachers of the schools. Lesson study engages teachers in creative and collaborative problem solving activity in designing a lesson that teaches mathematics through problem solving. The project is based on the following principles: (1) learners construct their own knowledge whether that learner is a teacher or a student; (2) learners learn most when they are engage in tasks that they view as significant to them and that presents a real problem for them; and (3) learning is a social activity whatever the object of the learning is.
Lesson Study in Philippines
The results of the lesson study project has been very encouraging. In terms of outputs, video lessons and lesson plans have been produced showcasing teaching mathematics via problem solving. These lessons were developed and implemented by the teachers collaboratively together with one UP NISMED mathematics education specialist per year level. The lessons produced show:
how to facilitate a problem solving lesson where students solve problems without being shown a solution first (the essence of the problem solving activity is preserved);
that a problem, traditionally given at the end of the chapter can be given at the start of the chapter;
that review of concepts, traditionally a separate part of the lesson and in drill type, can be integrated to the main lesson itself;
that lesson can be structured that would engage students to represent ideas mathematically, solve problems in different ways, and reason out;
that a problem solving task can be a rich context for learning new mathematical concepts and link these with previously learned concepts.
As a result of these, and this is perhaps the most important achievement of the project, is the change in the teachers’ perception about the role of problem solving in mathematics. During the planning meetings, the mathematics teachers I was working with expressed apprehension about the problem solving lesson they were developing. They said that “Work” problems are one of the most difficult types of algebra problems so they thought there is no way students can solve it by themselves without being shown sample problem and solution first and the even if these are shown, students still need to know how to solve rational equations. This is the reason why the problem is found at the end of the chapter! These were their impressions until they produced and implemented a lesson that challenged their own assumptions. They realized that problem solving can also be a means for learning mathematics rather than simply a reason for learning it; and, that students are more capable in solving problem on their own than they previously thought.
The teachers admitted that initially, they saw lesson study as another “burden” to them but as the project progresses they eventually appreciated it. They said that they learned a lot from each other and the post conference and discussion part became a venue for them to deepen their understanding of mathematics and how students understand mathematics. We also documented changes in the quality of teachers discussion during the post conference. Initially they were focusing on general pedagogy but towards the third cycle of the lesson implementation they were now more focused on the content and how their questions for discussion is affecting the quality of the students’ thinking.
This year we are working with another school with an improved design of the project. We just finished a three-day orientation seminar about lesson study and teaching mathematics via problem solving for the mathematics teachers of the said school. Goal-setting, the first step in the lesson study process was done during the seminar. The teachers agreed that their goal is to make students value mathematics by developing their thinking skills. Their sub goals for this year is to develop lessons that engage students in mathematical representations and solving problems in different ways. I will talk more about these in my next post.
Email me if you are interested to do lesson study in your schools (schools in Philippines only.) To give you an idea how lessons are planned and analyzed in a lesson study context view this presentation: Planning and Analyzing Mathematics Lessons in Lesson Study
Studies show that the way to go to implementing effective and sustainable educational reform will be through an inquiry-type professional development program and while the teachers are in action. One of these professional development models that has proven effective in Japan and is now being implemented and widely used in many countries is Lesson Study. It is also one of the identified factors for Japan’s high achievement in TIMSS.
Lesson Study engages teachers in creative and collaborative work in developing and researching a lesson through a “design-tryout-reflect-revise” cycle until it reaches a form to which they believe would be exemplary to them and to other teachers. It assumes that by investigating the teaching and learning process in the context of designing and implementing a lesson, it could provide teachers with experiences that has the potential to deepen their content knowledge and their knowledge about how students learn concepts and skills, develop teachers skills in designing and facilitating lessons, and most importantly develop the skills, habit and confidence in investigating their own lessons.
In the Philippines, the first Lesson Study project was implemented in 2006 by UP NISMED with selected mathematics classes. The project was called Collaborative Lesson Research and Development (CLRD) to give emphasis on the collaborative nature of designing and researching the lesson, something that is not yet a popular practice among teachers in our country. The objectives of the project were 1) to equip teachers with skills in designing mathematics lessons that engage student in mathematical thinking processes; 2) to enhance teachers’ knowledge of content and pedagogy as they study how their students think, learn, and reason; 3) to develop a lesson study model that is adaptable to Philippines classroom realities directly affecting teaching and learning of mathematics which include among others large class sizes, inadequate content and pedagogical content knowledge of teachers and insufficient materials and resources; and, 4) to gain insights about how teachers implement reform-based teaching strategies in their classes. The unique feature of this lesson study project in the Philippines is the focus on developing teachers capacity in designing lesson and teaching mathematics through problem solving, something that is also not yet a common practice of teaching mathematics in our classes.
