Posted in Assessment, Curriculum Reform

Teachers teach to the test, students study to the test

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The DepEd is finally bidding adieu to multiple choice test. Better late than never, I must say. So my fellow math teachers, the next time you are required to make purely multiple choice items for periodical test or are given by the division, or by the regional office an achievement test in multiple choice, you can quote the following: Annex A – The Monitoring and Evaluation of the Implementation of the 2002 Basic Education Curriculum: Findings and Recommendations of the UbD-based 2010 Secondary Education Curriculum Guide for Mathematics 1 document released by DepEd. On page 9-10 of the said document you will find this report:

 

9. Teachers teach to the test, students study to the test.

The use of traditional assessment tools like the multiple-response, simple recall, recognition and application tests is predominant.  Rubrics, portfolios, and other forms of authentic assessment are not widely used.  Teachers are aware of the limitations of traditional tests and the need for alternative forms to measure higher order thinking skills.  However, they tend to resort to the traditional forms for several compelling reasons:

  • These are the types used in periodic and achievement examinations.
  • They are easier to score.  (Teachers teach as many as 300 to 400 students a day and scoring non-traditional measures like rubrics could be an ordeal.)
  • They are easier to prepare than the non-traditional forms like portfolios, rubrics, and other authentic measures.
  • These are what everybody else is using.
  • Teachers have inadequate knowledge of authentic learning and authentic assessment.

Documentary analysis showed that schools in general lack an institutionalized system of utilizing test results for diagnostic and remedial purposes.

Teachers tend to teach to the test; students tend to study to the test.  This culture is reinforced by supervisors who specify units to be taught and tested for each grading period and use test results more for judging rather than improving teacher and student performance.

Recommendations:

Schools should review their present assessment practices.  The teacher appraisal system and the kinds of tests used in the classroom as well as those, in the division and national examinations, should be evaluated against the goals and objectives of the Basic Education Curriculum, among which is the development of critical thinkers and problem solvers.

Schools should also consider the use of alternative assessment tools and techniques that would provide opportunities for students to experience learning as an enjoyable, delighting process of inquiry, discovery, construction and creation of new knowledge, rather than as a tedious process of cramming to pass examinations.

While schools should double their efforts for students mastery of the basic competencies they should also never lose sight of the fact that their ultimate goal should be the development of functionally literate citizens of a democratic community.

I think the DepEd forgot to include another reason why teachers use multiple choice test. The sixth bullet should be: The National Achievement tests  in all subject areas are 100%  in multiple-choice type form and the test results are used more for comparing schools rather than as basis for developing programs for improving teaching competence and performance.

The day the National Achievement Test (NAT) of the DepEd will include constructed-response type questions should be declared a national holiday because it will really mark a turning point in the history of education in the Philippines.

Posted in Algebra, Trigonometry

Teaching trigonometry via problem solving

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I believe that the best way to learn mathematics is through solving problems. However, most problems are found at the end of unit or chapters. Because we are in a hurry to cover the textbooks or the curriculum, we skip the problem solving part and then we complain that our students are very poor in problem solving.

The only way to develop problem solving skills is by solving problems. The only way not to skip problem solving is to put it in the beginning of the lessons, use it in teaching the concept than as applications after learning the concepts only. I have shared sample lessons on teaching integers and algebraic expressions via problem solving in this blog. This time I’ll  share a trigonometry lesson through PowerPoint presentation. The lesson is an introductory lesson on tangent and cotangent. The lesson shows how you can introduce these concept as ratios and as functions.

Features of the lesson

  • Teaches via problem solving
  • The problems have many solutions
  • Links new concepts to previously learned knowledge
  • Problems are in real-life contexts
  • Shows geometric and algebraic (function) side of trigonometry
  • Students  compares and evaluates different solutions

The presentation shows the teacher the flow of the lesson.  Use it after the students have solved the problems in different ways, as a way of summarizing the possible solutions. Crucial to the lesson is slide #10 which contains questions for discussing the students’ solutions and the link between the previously learned concepts and the new concepts introduced in this lesson.

Teaching trigonometry

 

Posted in High school mathematics, Lesson Study

Pedagogical Content Knowledge Map for Integers

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I’m working with a group of Year 7 mathematics teachers doing Lesson Study for the first time. The teachers chose to do a lesson study for what they believe to be the most difficult topic in this year level – integers. Part of my preparation as facilitator is to draw a map of what I know about teaching the topic. The map is more than a concept map because it includes not just related big ideas or concepts but also how  these are taught and learned. Hence, I call this pedagogical content knowledge map (PCK map).

The PCK map I present here is a product of my own readings and my own experiences of teaching the topic. This means that it may not be the same as other teachers especially the ‘teaching part’ of the map, the ones in orange colors. For example, experience and research results back my claim that the number line is a very good way of representing the set of integers but not in teaching operations. Click here for my post about this. Notice that I gave emphasis on students knowing when a negative, a positive or a zero result rather than the rules for operation. I believe that without this, a conceptual understanding of the operation involving integers will be weak. Also, experience has taught me that although integers are numbers, the teaching of it must be algebraic. The instructions should be so designed so that students are learning algebraic thinking as well. I have noted this in the PCK map.

The map is not yet complete. I intend to include descriptions of effective activities and students’ learning trajectory of the concept after my research with the teachers. Please feel free to give your comments and share experiences for teaching integers that I could look into in my study.

pedagogical content knowledge
PCK Map for Integers

Please click the link to see my PCK map for Algebraic Expressions.

Posted in Lesson Study, Mathematics education

Lesson Study in Mathematics

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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.

Download full paper: Scaffolding Teacher Learning through Lesson Study.

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