By Deia Sanders
By all counts of the system, I was an excellent teacher. When the average middle school growth was 5 QDI points, my classes always grew 25-27 points. There were teachers in our district and state that did the same or better each year.
But when I think back to what we were measuring, I can’t say I prepared students to exceed in mathematics in the real world. I can’t even say I prepared them for college. I brought as much real-world experience as I could into the classroom, and I taught mathematics with every inch of my knowledge and expertise, but in the end, what measured their knowledge was a test that could be “outsmarted.”
I recently worked with some very knowledgeable and experienced mathematics teachers. We talked about how teaching one unit under the new standards would prepare kids for high school, college, and the real world better than a year under the old ones. We also discussed how a student could pass a mathematics standard, or even a test without actually knowing how to complete the skill being tested. We trained students that in a multiple-choice test, the answer was already there. As teachers, we would say that we wanted the students to work it out, but in the end, if they forgot everything they learned in class, we would tell them to just start trying your options in the multiple choice and see which one works.
For example, here are some practice questions from the current Mississippi state test, MCT2.
Do you see that a student could “plug in” answers until they determined the correct one? They don’t have to write an equation or work steps to solve an equation. In this discussion with teachers, one of them even noted that a review for MCT2 they noticed all but 2 questions in the review could be solved without actually performing the mathematical skills it was testing. Myself and the other teacher also had the same experience when teaching and reviewing in previous years. That’s not even mentioning that if you do nothing but close your eyes and pick one you still have a 25% chance of getting it correct, or that we had classes on “test-taking skills” which focused on eliminating answers so that you had a 50/50 chance of guessing the correct one.
So here we were, reviewing the new standards and finding sample questions to test them, realizing that although we had all been “successful” under the current system, we now realized that our standards were low, and successful by these terms did not equal success in the future. We discussed how difficult it was for our students who had been trained for years to “plug in” answers to transition to actually having to work and use the skills they were taught to solve problems. To use multiple standards together to solve problems. To be given a scenario and have to write equations, name the property used, solve equations, compare to another scenario, etc…. The real world is not likely to come with multiple choice options to plug in, so we know as educators we are now on the right track, but we know this transition will be difficult for all involved. Fortunately, everyone agreed that the students seem to be improving and adapting quickly.
When I think back to my marketing career, I used a lot of algebra to determine spending and budgets of other companies. I took what I knew about their spending to determine what I was missing in their budgets, and at no time did an ad agency say “I can’t tell you my budget, but I will give you some options to 'plug in' and figure it out.” I know from what I’m seeing in the classes and from my experience in the real world that we are finally preparing students for what lies ahead in their life.
A task or math problem assessing equations in a current mathematics classroom is more likely to look like this than the previous examples.
Kimi and Jordan are both working during the summer to earn money in addition to their weekly allowances, and they are saving all their money. Kimi earns $9 an hour at her job, and her allowance is $8 per week. Jordan earns $7.50 an hour, and his allowance is $16 per week.
(a) Complete the table below:
(b) Write an equation that can be used to calculate the total of Kimi’s allowance and job earnings at the end of one week, given the number of hours she works.
(c) Write an equation that can be used to calculate the total of Jordan’s allowance and job earnings at the end of one week, given the number of hours he works.
(d) Sketch the graphs of your two equations on a pair of axes.
(e) Jordan wonders who will save more money in one week if they both work the same number of hours. Write an answer for him.
Which one do you think will truly measure a student’s ability to write and solve equations? Which kid is less likely to be taken advantage of in the future? Which kid would you want to hire? A child who could pass the multiple-choice questions with no problems, or one who may waver a little, but could work through the second set of questions? As an educator, I know which one would truly measure what I taught in a classroom.
Is it going to be more difficult for the teachers? Yes. Students will have to solve multi-step problems and in some cases know what they are doing enough to explain why one option is better, more reasonable, or more efficient than the other. Is it more difficult for students? Yes, there are no loopholes or tricks for when you don’t know how to solve the mathematics. Is it more difficult for parents? Yes, more is being asked of their child. Although it may be that we want a deeper understanding, it doesn’t make it easy to watch your child who may have always had A’s suddenly have to study or struggle to keep them, or even slip to B’s. Raising the bar is always challenging.
If I had to compare education to my personal life, I would compare it to running. Most people can run or walk a 5k. They are usually local and small events. I really enjoy running 5ks because I know I can be successful at it. I could run that distance several days a week, and have even won a medal in my age group in a 5k. When I wanted to take my running to the next level I decided to train and run a half marathon. In the half marathon event, I am now compared to thousands. The training was different and more difficult. I had to focus more and for the first time I had to deal with injuries and setbacks. I’m no longer going to come home with a medal showing I placed, but am I better than I was before? I was running 3 miles and now I’m running 13 miles; of course I’m doing better! Does the lack of a medal even matter if I know I am improving? Was it difficult at first? Absolutely! But the good news is that when you are working towards a goal, you generally reach it. Being challenged isn’t a bad thing. There are days when I thought I’d never run my first half marathon, and now I’m getting ready for my fourth. Long runs just became normal. I know we are in a transitional time where it seems like the challenges are overwhelming some days, but one day this will just be normal, too. That’s how meeting challenges works.
*MCT2 Practice Test
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