Tag Archives: solving equations

“Too Bad We Can’t Find Out Which Way Works Best.”

“It’s too bad someone can’t do a study to see which way (direct instruction or hands-on learning) works best.”
This comment came from a colleague in a discussion on how well my remedial Algebra class did with the assessment on a particular non-traditional lesson. Before I share my thoughts on this, let me offer some background on the class and some data.

The demographics of the class is quite challenging: 4 SDC (special day/workshop), 5 ELL (english language learners), 7 IS (special ed), 5 Academy (highly at-risk), out of a total of 30. While the others don’t have an acronym after their name, they still have a history of struggling in school. And I absolutely love teaching this group! I share all this first, because the data I am about to show will be all that much more impressive.

I began our previous unit on Solving Equations with a pre-assessment of the 6 types of equations that they were going to learn to solve:

1) x + 4 = 31
2) 4x = 28
3) 7x + 5 = 26
4) 10x + 2 – 4x = 44
5) 11x – 4 = 3x + 12
6) 9(x – 2) = 45

Then I spent a week of direct instruction (D.I.) and 2 days with the simplifying and linear equations components of the Truffles lesson, after which I assessed them for a second time on the same 6 equations. I then led the students through the Hippity-Hoppity lesson for 4 days, and assessed them again on the same 6 equations. The progression of results is shown below. (There are only 22 students shown due to the shuffling of students classes at the beginning of the year.)

 # correct Pre-
Truffles & D.I.
6s 4 13 19
5s 4 7 3
4s 3 1 0
3s 3 1 0
2s 3 0 0
1s 2 0 0
0s 3 0 0

My class went from only 36% getting 5 or 6 correct, to 90% after the Direct Instruction and Truffles lessons, to 100% after the Hippity-Hoppity lesson. It is worth noting that the number of students correctly solving all 6 equations rose from 59% to 86% after the last “active-learning” activity.

My friend made his “too bad we can’t find out which way is best” comment having only heard about the last lesson, not knowing the work I put into the unit throughout. That work demonstrates a variety of strategies that might be classified as direct instruction or hands-on learning. He didn’t realize that I had implemented several ways, not just one.

I utilized several strategies because there is a great deal of research that shows that the best way is a balanced approached. However, that balanced approach is not between methodologies (direct instruction vs discovery/hands-on/active learning); it is between skill acquisition and critical thinking. I chose to use lectures and guided practice to impart skills, the Truffles lesson to instill understanding of a variable, and the Hopping lesson to offer an application of the topic. These last two lessons also required my students to practice other skills that they lack: reading and writing in a mathematical context, and following multi-step directions.

So we should tell all of our colleagues that we do indeed know a best way. It is not my way, your way, or their way, but a balanced way.