Katha 2014: Lesson Study as a professional development model

Minutes of the workshop transcribed. Speaker Sir Levi

KATHA 2014: Day 3:

LESSON STUDY as a professional development model

Mr. Levi

Minutes of the Workshop

Mathematical knowledge should be redefined and reconceptualize for the students to be able to grasp its essential components and comprehend and appreciate at the same time the field that has been long way conditioned to be stigmatized. The speaker first presented the Characteristics of Mathematical tasks in the cognitive level of a low level task, compared to a high level task.  The speaker proposed a task analysis and problem set for the participants by letting them think of high-order mathematical questions and problems for their students.

During the evaluation of the task, the teachers said that their main goal is to retain the most basic concept in the students’ mind and develop their critical thinking. One of the teachers presented a dilemma where learners tend to think that Math is already difficult as it is. The speaker presented a solution: LAS; that is, this is to imbibe the students to Love All Subjects and impose it as a school policy. Another teacher explained that there is a difficulty in the basic operations in the students. Another raised the issue of planning the lesson study for the day, if the topic should be one by one or by integration. The speaker explained that it would be better if the teachers first give the problem set to the students to reflect on before presenting the lesson for the day. One teacher said that students also tend to forget the lesson of the previous session, and the speaker explained that this is because the students are honed to memorize the topic instead of understand its basic concept. It would be better, furthermore that the teachers let the students discover the solutions and conclusions to the previous problem sets so that they will be able to remember the lesson better.

More solutions to the problems presented by the teachers during the evaluation include letting students discover multiple solutions to the problem set, make math learning fun for them and give them small incentives once they improve on their skills.

The speaker also presented general truths regarding Math teaching and lesson study: 1) Heterogeneous classes are very hard to handle. This is to mean that not all students will be able to grasp the basic concept all at once. 2) Teachers are forced to fit to the basic and traditional curriculum standards, which will be very hard to penetrate especially because improving lesson study is exactly the opposite method of the traditional lesson study planning. 3) Student attitude is typically reluctant with low confidence over a problem set because of the conditioned stigma and the deemed difficult problem sets. This is one problem that should be specifically addressed. 4) Teachers have no guts or the opportunity or the time to do proper mathematical teaching.

The speaker proceeded to discuss the Problem Set Analysis, which would help scaffold the lessons for the slow learners and be expanded for the advanced students. He proposed that there should be collaborative groups for the students, outline expectations and identify one lesson topic for each group, identify exercises with potentials, access the difficulty of the questions and illustrate samples of deep and challenging problem sets to the students. Given the traditional books in school, the teachers may revise the textbook questions to problem task analyses. The may also discuss concepts of different math topics without really using jargons and technical terms. Finally, it would be effective for the teachers to let the students arrive at the conclusions of patterns and discovery of solutions. That is, they have to let the students make sense of the problem, reason abstractness, and construct their own concepts.

The speaker followed the discussion with Performance Scores. This topic includes the rubrics, descriptions of benchmarks and evaluation of the level of proficiency of the student in their mathematical skills. The speaker presented this lesson study by providing problem sets to the teachers in five ways:

1) Comparing Numbers by 100 000. This activity may be discussed using number cards and use elements of surprise as well. This can be applied to Grade 2 and above. This activity identifies and enhances the learning capacity of the students and at the same time scaffolding the lesson plan to avoid curriculum congestion, which is a number one problem in the traditional curriculum. It would also be better if the teacher uses the lesson plan as part of the puzzle for the lessons of the week; that is for integrated learning.

2) Exploring Numbers with 10 000. Teachers may use guide questions to scaffold and extract patterns and similarities from students based on their own concepts. The teachers should also let the students generalize and find their own solutions and patterns. This may be applied to different topics in subtraction, place value and addition as well, which can all be integrated into one lesson study for the week.

However one teacher raised the issue of the complexity of the integrated lesson study which he thought would confuse the students just as much as the teacher would be confused especially on his lesson study for the week. But then the speaker pointed out that was exactly what the old curriculum had been inhibiting the teachers and students to think in high order critical thinking,no integration and connections on the topics in mathematics.

3) Looking at Multiplication Errors. Teachers may give out questions for the students and applying the technique of Cuisinaire Rods; that is, using fractions, grouping the students by problem sets and letting them come up with their own generalizations.

4) Fractions as Percentages. Teachers may apply paired grouping in this lesson study and draw models to illustrate fractions to integrate with percentages (using proper and improper fractions). This may also be the time to scaffold terms used previously.

One teacher raised a question on the structure of the lesson plan and how to apply the lesson proper. The speaker said that the ultimate end product of lesson study is assessment and evaluation of the student’s knowledge in the different math problem sets presented for the day. This he said is termed as the problem-structured approach.

5) Average and Making Connection. Teachers may illustrate integration of the topics in math to both cater slow learners and advanced students; also by using extension questions. Teachers may also use pattern mobiles by using cut-out shapes of the different topics in math for the week.

Finally the speaker left the participants with an activity on formulating high level tasks for their classes for one week, by using the lesson study problemstructured approach, guide questions, multiple choice questions and report on its implementation.