IMPpg1

Program Organization and Structure

The IMP curriculum is a core curriculum that is intended for all high school mathematics students. It is a curriculum that can be worked through at a fast, slow, or normal pace (the pace suggested in the text). However, I do not think that students with all different levels of mathematical abilities should be placed within one class. The advanced mathematics students should not be placed with those students who have difficulty with mathematics. The pace of the curriculum needs to mach the mathematical ability of the student.
The IMP curriculum is separated into four years. Each year is composed of five units. Each of these individual units covers a variety of related mathematical topics, usually falling within one strand of mathematics. By organizing the curriculum in this way, most of the major strands are studied every year.

Content

At the beginning of most of the units, a problem is presented for the students to solve. Each day they work on a concept that will give them the skills and knowledge they need to have in order to solve the unit problem. Each day they build upon what they learned the day before, and thus, they keep moving forward. By the time the students reach the end of the unit, they are asked to solve the unit problem.
Throughout the four years, references are made back to the previous units. For example, in the fourth year there is a unit called "High Dive." It involves mostly concepts from trigonometry. As the students move forward throughout the unit, they will come across quite a few references to one of the units titled, "Do Bees Build it Best" form the 2nd year. This particular unit covered geometric ideas. The curriculum does this to refresh the students memory of concepts already make mathematical connections to previous concepts, and to build deeper understanding.
Another good example that shows how the units are connected throughout the curriculum is in the fourth year. At the very end of the "High Dive" unit, which covers trigonometry, they ask the students to revisit a unit from the first year, "The Pit and the Pendulum." The textbook proposes another problem that is a variant of the one they solved in their first year. This time, they are asked to use what they learned from the unit they just completed to solve this different and more complex version of a problem they had done 3 years prior. The "High Dive" unit involves ideas from trigonometry, while the "Pit and the Pendulum" involves ideas from statistics. This example shows how different mathematical strands are connected throughout the curriculum.
There is also a teachers manual for each year that is specifically for graphing calculators. This manual allows teachers to integrate technology into the classroom. There is your basic "button pressing" in there, but there are also ideas that can promote higher levels of thinking. For example, there is a prime number extension activity which helps students find and understand prime numbers. The book also has a programming section to show students how to write the prime number program.

Instruction

This curriculum makes use of a variety of instructional methods. The teacher’s manual gives an outlined description of each class period. The outline usually suggests that the only time the teacher leads the class is to go over homework and to bring the class back together for discussion after the investigation. The group investigations are where the students are in small groups to work through the activity, or solve the problem(s) given. This is usually where the students are working together in small groups. In this setting the students are talking, thinking, and solving together. This type of classroom environment is very student centered.

Learning

In the classrooms that use IMP, students are not "told" mathematics. The textbooks that they are given have been designed to guide them in discovering mathematics themselves. With the textbook as an outline, and the teacher as a facilitator, the students come up with their own conjectures and test them, come up with general formulas, create their own algorithms, make definitions, and basically learn the material through discovery. To accomplish all of these tasks, students frequently (almost daily) work in small groups.
As a team, they think together, communicate together, draw off of each others ideas, determine multiple ways to solve problems, work out difficulties, ask and answer questions, and make more connections.
As mentioned previously, everything that is done in class must be justified. They must explain what techniques they used, what the group was thinking about when they did this, what they did when it didn’t work, etc.… By discovering mathematics on their own, the level of understanding is much deeper than if they were just "told" it.

Assessment

Assessment is integrated throughout the curriculum. By requiring students to explain every thing that is done, this allows the teacher to see what the student does or does not understand. Also, there is a POW section that is integrated throughout the text book. This is a proof exercise. The teacher’s manual includes suggested rubrics for these exercises. The daily homework consists of mainly short answer questions that apply and extend what the students may have learned on that particular day. The questions require the student to think about what they did that day, and relate that information to different scenarios. A few computations show up, but they are never without the question, "Why?" The homework is often where the students formulate the general rules and definitions about the days work. If an algorithm does exits, sometimes the students are asked to determine it.
At the end of each unit there is a unit test. The unit test is composed of an in class portion and a take home portion. The in class assessment is one scenario with a few questions to answer. For the test, students are allowed to use notes, calculators, or previous work. The unit tests take what the students have learned and ask them to apply it in different ways. Also at the end of each unit, the students are required to make a unit portfolio. In here they put all the important work they did, and write all of the important concepts learned. If there were any algorithms, formulas, or definitions that needed to be remembered, it is to be put in the portfolio. Not only is this an excellent assessment tool, it is a very useful tool for the student. It is a reference guide that is referred back to throughout the whole curriculum. NEXT -->