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.
2nd International Conference in Science and Mathematics Education via kwout
The University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED) will hold its second international conference in science and mathematics education on October 26-28, 2010.
The conference will feature plenary sessions, symposia, paper presentations, poster presentations, and workshops.
Click link for details or email me: erlines@ymail.com
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
Not many teachers make an issue about curriculum framework or standards in this part of the globe. The only time I remember teachers raised an issue about it was in 1989, when the mathematics curriculum moved from compartmentalized (elem. algebra, intermediate algebra, geometry, adv. algebra & statistics) to spiral-integrated approach. The reason behind the change was the poor performance of the students. Many teachers didn’t like the change in the beginning not only because it’s the first time that the mathematics curriculum is organized that way, hence new, but also because it demands re-learning other areas of mathematics which they have not taught for years. Also, teachers were not taught mathematics in high school nor in college that way. But the curriculum was pushed through just the same and eventually teachers complaints about it died down. Why? No one knows. They just continue teaching what they know in the way they think best.
Sometime in late 2001 or was it 2002, the then secretary of DepEd made a phone call to one of the country’s math education consultants. The country’s students seem not getting any better. Something’s got to be done about it. So one day, in 2002, the country’s basic math community woke up with a new curriculum, back to the compartmentalized system. The identified culprit according to the sponsor of the compartmentalized curriculum was that teachers are not that capable yet to implement the spiral-integrated curriculum that is why the still low students’ achievement. Clearly teachers need upgrading in their content knowledge and pedagogical knowledge and they need a lot of support resources for teaching. The solution made to this problem? Change the curriculum. In fact not only to change it back to where it was but DepEd reduced the content further to minimum competencies consisting of learning of facts and procedures, a sprinkling of problem solving and an inch thick of content for mathematics. Did the teachers like it? Did it work? No one knows. They just continue teaching what they know in the way they think best.
It’s 2010. The minimum learning competencies lived up to its name. It provided minimum knowledge and skills. The students’ achievements did not get any better.
By June this year, the Math 1 (Year 7) teachers will be making their lesson plans based on UbD. UbD or Understanding by Design is the title of a book which proposes a new way of doing curriculum planning. In the school level, its in the way the teachers will be preparing their lesson plans. UbD is based on backward design. The main difference between backward design and the usual way of writing the lesson plan is that you spend time first formulating how you will assess the students based on your identified goals (aka enduring understanding and essential questions using UbD lingo) before thinking about the activity you will provide the class and how you will facilitate the learning. I’ve yet to see and read a report from the proponents and users of UbD for evidence that it really works. And working in what aspect? in which subject area? and, whether it is better than the usual way teachers prepare their lesson plan? Some schools who have tried it reported that at first, teachers had a lot of difficulty in making a UbD-based plan but they eventually got the hang of it. Are they teaching any better? Are the students doing well? Silence. I’m asking the wrong questions. For indeed, a great distance exist between way of preparing lesson plans and students’ achievement. So why are schools all over the country mandated to adopt UbD? I don’t know.
But this is what I know. I know that teachers need support in upgrading and updating their knowledge of content and pedagogy. I know that teachers teach what they know in the way they know. These are things that cannot be addressed by simply changing the curriculum or changing the way of preparing the lesson plan, much more its format. The book The Teaching Gap which reports the TIMSS 1999 video study tells us what we should focus our attention and resources more on:
“Standards [curriculum] set the course, and assessments provide the benchmarks, but it is teaching that must be improved to push us along the path to success” (Stigler & Hiebert, The Teaching Gap, p.92).
I couldn’t agree more to this statement. I’m not very good at memorizing so to commit it to memory I paraphrased Stigler & Hiebert’s statement to: It’s the teaching, stupid.
