**What is the best way to structure a Maths lesson?**

It is many years since I have written up a formal lesson plan – but of course all teachers plan their lessons, both on paper and in their heads. [A teacher I know claims he uses a 39 step lesson plan. That’s how many paces there are from his office to the classroom!] Of course a good teacher can change the course of a lesson as the need arises.

An excellent starter to this discussion is the web article: ‘How does a Japanese math lesson differ from the conventional U.S. math lesson?’ This draws on the TIMSS research which suggest these structures:

**United States & Germany**

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.

**Japan**

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.

In Australia, use of the US model is also widespread, but various innovations in Mathematics teaching have started to lead us towards the Japanese model. egs. MCTP and Maths300. Indeed some text books were written that presented a problem at the start of each chapter.

Is the greater success rates in Mathematics due to this model? Possibly but I’m sure that there are many other influencing factors as well. However, one contrast between these approaches is that the Japanese model involves much higher order thinking skills. i.e. the students do more thinking rather that just copying the teacher.

The ‘Intel Teach to the Future’ project further emphasises the importance of designing lessons that require higher orders of thinking. The lesson planning process is:

Intel units are an example of PBL (Project Based Learning) and have the following features:

**1. Students are at the centre of the learning process.****
**2.

**Projects focus on important learning objectives that are aligned with standards.**

**3.**

**Projects are driven by Curriculum-Framing Questions.**

**4.**

**Projects involve on-going and multiple types of assessment.**

**5.**

**The project has real-world connections.**

**6.**

**Students demonstrate knowledge through a product or performance.**

**7.**

**Technology supports and enhances student learning.**

**8.**

**Thinking skills are integral to project work.**

**9.**

**Instructional strategies are varied and support multiple learning styles.**

The last feature is also important as the US model is fairly one dimensional in the way the teaching is delivered. I would dare to say that use of a wide variety of instructional strategies and assessment methods is just as important as the structure of a lesson.

Finally, consider the following problem presented in two different ways:

1. Expand brackets and solve for “n”:

2. Find 5 consecutive integers such that the sum of the squares of the first three integers, is exactly equal to the sum of the squares of the last two integers. How can you be sure that you have found all possible solutions?