Sunday, February 16, 2014

Japanese Math Lessons

Japanese teaching - TV Show


Actual Japanese Math Lesson:


Beginning of Japanese Math lesson (the other segments are on YouTube:

What do U.S. mathematics lessons look like? One of the most exciting aspects of TIMSS is the opportunity to learn more about teaching in other countries. Some preliminary findings from the TIMSS video study into which we will want to inquire further are the following: The structure of U.S. mathematics lessons is similar to lesson structure in Germany, but different from that in Japan. The study reports that eighth-grade lessons in Germany and the U.S. emphasize acquisition of skills in lessons that follow this pattern:

1. Teacher instructs students in a concept or skill.

2. Teacher solves example problems with class.

3. Students practice on their own while the teacher assists individual students. [1, p. 42]

 In contrast, the emphasis in Japan is on understanding concepts, and typical lessons could be described as follows:

1. Teacher poses complex thought-provoking problem.
2. Students struggle with the problem.

 3. Various students present ideas or solutions to the class.

4. Class discusses the various solution methods.

5. The teacher summarizes the class' conclusions.

6. Students practice similar problems.

"Bansho" means Japanese blackboard. This idea was imported from Japan and was the missing piece I struggled with the first few times I tried three part lessons. This is how it works...
I had my first group come up and share their answer. I chose the group that had the weakest answer to go first. They only had their names on the page and had spent most of the time bickering so they didn't really have an answer or strategy at all. However, I didn't discuss that fact, only allowed them to present their ideas. After that, I posted in on the left side of the whiteboard. Then I had the second group do the same; this group had an answer, but had made some mistakes and were missing some components. Again, they presented and I posted it to the right of the first answer. The third and fourth groups did the same, with their answers increasing in depth and thoroughness. Once all the answers were posted, we went back to the first and looked at each critically. My questions to the class were "What does this answer have that we need?" and "What is this answer missing?"  I wrote on the board under each question the things they included successfully and the things that were missed. One of the students from the second group even explained were they made their mistake. I focused on the number of strategies they used and the components (strategy, number sentence, answer in words) that were included, rather than on whether or not the answer was correct. At the end, they could clearly see what made for a successful and thorough answer and which level each answer would earn on an assessment. from

More on Bansho:

Three part lesson based on Japanese teaching:



Thoughts on Teaching Math

1. Only five percent of mathematics should be learned by rote; 95 percent should be understood.
2. Real learning builds on what the child already knows. Rote teaching ignores it.
3. Contrary to the common myth, “young children can think both concretely and abstractly. Development is not a kind of inevitable unfolding in which one simply waits until a child is cognitively ‘ready.’” —Foundations for Success NMAP
4. What is developmentally appropriate is not a simple function of age or grade, but rather is largely contingent on prior opportunities to learn.” —Duschl & others
5. Understanding a new model is easier is you have made one yourself. So, a child needs to construct graphs before attempting to read ready-made graphs.
6. Good manipulatives cause confusion at first. If a new manipulative makes perfect sense at first sight, it is not needed. Trying to understand and relate it to previous knowledge is what leads to greater learning. —Richard Behr and others.
7. According to Arthur Baroody, “Teaching mathematics is essentially a process of translating mathematics into a form children can comprehend, providing experiences that enable children to discover relationships and construct meanings, and creating opportunities to develop and exercise mathematical reasoning.”
8. Lauren Resnick says, “Good mathematics learners expect to be able to make sense out of rules they are taught, and they apply some energy and time to the task of making sense. By contrast, those less adept in mathematics try to memorize and apply the rules that are taught, but do not attempt to relate these rules to what they know about mathematics at a more intuitive level.”
9. Mindy Holte puts learning the facts in proper perspective when she says, “In our concern about the memorization of math facts or solving problems, we must not forget that the root of mathematical study is the creation of mental pictures in the imagination and manipulating those images and relationships using the power of reason and logic.” She also emphasizes the ability to imagine or visualize, an important skill in mathematics and other areas.
10. The only students who like flash cards are those who do not need them.
11. Mathematics is not a solitary pursuit. According to Richard Skemp, solitary math on paper is like reading music, rather than listening to it: “Mathematics, like music, needs to be expressed in physical actions and human interactions before its symbols can evoke the silent patterns of mathematical ideas (like musical notes), simultaneous relationships (like harmonies) and expositions or proofs (like melodies).”
12. “More than most other school subjects, mathematics offers special opportunities for children to learn the power of thought as distinct from the power of authority. This is a very important lesson to learn, an essential step in the emergence of independent thinking.” —Everybody Counts
13. The role of the teacher is to encourage thinking by asking questions, not giving answers. Once you give an answer, thinking usually stops.
14. Putting thoughts into words helps the learning process.
15. Help the children realize that it is their responsibility to ask questions when they do not understand. Do not settle for “I don’t get it.”
16. The difference between a novice and an expert is that an expert catches errors much more quickly. A violinist adjusts pitch so quickly that the audience does not hear it.
17. Europeans and Asians believe learning occurs not because of ability, but primarily because of effort. In the ability model of learning, errors are a sign of failure. In the effort model, errors are natural. In Japanese classrooms, the teachers discuss errors with the whole class.
18. For teaching vocabulary, be sure either the word or the concept is known. For example, if a child is familiar with six-sided figures, we can give him the word, hexagon. Or, if he has heard the word, multiply, we can tell him what it means. It is difficult to learn a new concept and the term simultaneously.
19. Introduce new concepts globally before details. This lets the children know where they are headed.
20. Informal mathematics should precede paper and pencil work. Long before a child learns how to add fractions with unlike denominators, she should be able to add one half and one fourth mentally.
21. Some pairs of concepts are easier to remember if one of them is thought of as dominant. Then the non-dominant concept is simply the other one. For example, if even is dominant over odd; an odd number is one that is not even.
22. Worksheets should also make the child think. Therefore, they should not be a large collection of similar exercises, but should present a variety. In RightStart™ Mathematics, they are designed to be independently.
23. Keep math time enjoyable. We store our emotional state along with what we have learned. A person who dislikes math will avoid it and a child under stress stops learning. If a lesson is too hard, stop and play a game. Try the lesson again later.
24. In Japan students spend more time on fewer problems. Teachers do not concern themselves with attention spans as is done in the U.S.
25. In Japan the goal of the math lesson is that the student has understood a concept, not necessarily has done something (a worksheet).
26. The calendar must show the entire month, so the children can plan ahead. The days passed can be crossed out or the current day circled.
27. A real mathematical problem is one in which the procedures to find the answer is not obvious. It is like a puzzle, needing trial and error. Emphasize the satisfaction of solving problems and like puzzles, of not giving away the solution to others.