The MTGK Curriculum is designed to reinforce conceptual and abstract thinking, while still providing real world examples and word problems for students to tackle. Algorithmic methods are approached step-by-step and explained. Variables are introduced as early as grade 2. Word problems reinforcing the concepts are demonstrated in every unit. Topics are discussed, and revisited year after year.
Targeting elementary, middle and high school students to get ahead in math conceptual thinking
For example, the multiplication algorithm is demonstrated in grade 3:
7 1 7 0 + 1
× 6 × 6
4 2 6 ? 4 2 0 + 6
This is the distributive property in action! Though not explicitly stated, the concept is there. The curriculum guides students into understanding what is happening through a simple example, and no mention of the property is made. This is important for building recognition and familiarity with the abstract mathematics that comes later.
Then, we revisit conceptually in grade 4 through problems such as this:
Compare the answers for:
23 × 4 + 23 × 6 and 23 × (4 + 6).
Of course, in the classroom, students will be asked to calculate the problem on the left first. Almost all of them will multiply each individually and then add the results. This is how they are conditioned in schools to tackle these problems. But then, our teachers present the second case. They know the order of operations, and see that the answer is not only easy to calculate, but the same as the first. We can see now that the distributive property is at work, and is reason behind both sides being equal. Additionally, there is a reward to the students for using the distributive property: the problem on the right is easier to solve!
So finally, we can formulate through taking examples and noticing patterns that
A × (B + C) = A × B + A × C.
In the end, our curriculum takes this further, ultimately deriving the process of FOIL for taking the product of two sums that is taught during high schools when dealing with factoring and expanding quadratic equations. This is the exposure that our curriculum provides to our students. Learning is a process of making the unfamiliar familiar. Thus, we expose and re-expose our students to key concepts through a fantastic build-up of problems designed not only to be practice, but to do half the teaching as well.
See below for more detailed information on our curriculum.