Posted in Curriculum Reform, Mathematics education

What is 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.

The first step in doing lesson study is to articulate the goals for doing the lesson study. Click the link to read how I facilitated a group of teachers to identify their goals. It was their first time to do a lesson study. I reported the result of this study in the post Lesson Study for Teaching through problem solving.

Posted in What is mathematics

Math is not easy to learn – that is a fact.

I think it’s a waste of time trying to make math easy and fun to learn if your idea of fun does not involve challenge.

Mathematics is not an easy subject and it is not easy to learn it. That is a fact. The sooner the teacher accepts this, the better for her students. The challenge to us teachers is not in how we can make math easy to learn but in how we can make it makes sense and how we can make our students love the challenge that mathematics presents. Can math be challenging if students feel that what they are expected to do in the class is to follow the teacher’s method, the teacher’s way of thinking, and the teacher’s way of doing things? Where is the fun in that?

Mathematics is not fun to learn if the idea of fun is like playing bingo! However, if ‘fun’ is a function of the challenge a sport or a game presents, then indeed learning mathematics is fun. We love a sport because of the challenge it presents, the opportunities it gives us to make prediction, analyze, strategize, make our stand and defend it, etc and not because it is easy to play!

Everything in mathematics makes sense. Everything in mathematics is connected to everything else. I think this is where we teachers should be devoting our time to. And this is what this blog is about!

Posted in Assessment, Curriculum Reform, Elementary School Math, High school mathematics, Number Sense

Assessing conceptual understanding of integers

Assessing students’ understanding of operations involving integers should not just include assessing their skill in adding, subtracting, multiplying and dividing integers. Equally important is their conceptual understanding of the process itself and thus need assessing as well. Even more important is to make the assessment process  a context where students are given opportunity to connect previously learned concepts (this is the essence of assessment for learning). Because the study of integers is a pre-algebra topic, the tasks should also give opportunity to engage students in reasoning, number sense  and algebraic thinking. The tasks below meet these criteria. These tasks can also be used to teach mathematics through problem solving.

The purpose of Task 1 is to encourage students to reason in more general way. That is why the cells are not visible. Of course students can solve this problem by making a table first but that is not the most ideal solution.

adding integers
Task 1 – gridless addition table of integers

A standard way of assessing operations involving integers is to ask the students to perform the operation. Task 2 is different. it is more interested in engaging students in reasoning and in developing their number and operation sense.

subtracting integers
Task 2 – algebraic thinking and reasoning in numbers

Task 3 is an example of a task with many possible solutions.  Asking students to find a relation between the values in Box A and Box B links operations with integers to the study of varying quantities or quantitative relationship which are fundamental concepts in algebra.

Task 3 – Integers and Variables

More readings about algebraic thinking:

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