Although this idea applies at any age level, I am going to direct at the age I work most closely with – high school students. Most of my students are North Carolina students taking the new Common Core 1, 2, and next year they will start Common Core 3. I am slowly watching as the scope and sequence that North Carolina has chosen unfolds for each level. Common Core 1 contains many Algebra 1 topics and Common Core 2 is more heavy on Algebra 2 than on Geometry. I find that many of my students can do the work in isolation. By this, I mean, I teach them a topic – for example solving exponent equations that do not require logs: 3^(x+1) * 9^(2x -3) = 9^(3x+4) and once I teach the topic, they get it and are able to do it! They can complete a full page of work and get the answers right. The next day, students will come in with another topic, maybe finding the inverse of functions. I teach them the rule (exchange x and y, solve for the new y). They then do a page of those problems correctly. Prior to the test, students get many different topics in “isolation” from their teachers that we cover and they are successful at. However, when the test comes, they fail! Why?

Students don’t remember which problems require which steps. They don’t spend time memorizing what type of problems match which type of problem solving skills and they seem to lack the ability to just look at a problem and use their overall knowledge of math (a long list of other math skills they have forgotten from previous years) to be able to reason out the answer. Many times, they don’t even know what the question is asking.** ” Oh, I did a page of problems where I switched x and y and then solved for the new y, but that was called an INVERSE?”**

How do we fix this? Well, it really needs to be fixed retroactively as students need to remember all their old skills as they move on and apply the new skills. If one of their problems has a (1/81) and they are supposed to covert that to 3 to a power in Common Core 2, but they forgot all about negative exponents they learned in Common Core 1, then they are adding double the work. They have the new skill to learn about solving the exponent equations and they have to re-learn all their exponent rules. Hopefully, they are just “dusty,” and it doesn’t take too much and you can remind them that fractions mean negative exponents.

Moving away from the retroactive problem, let’s just focus on the best fix we can do. When teachers assign homework, they assign a page of all problems from the current isolated area. Solve 15 problems of exponent equations on Monday, solve 15 problems of inverses on Tuesday, solve 15 problems of solving radical equations on Wednesday, etc. If in addition to this, teachers each night gave students a sheet with one question from each area to solve and the “wording” of how it will be asked of them – for example, in trig, we say, “Solve the triangle.” What does that mean? It means find all sides and angles, well if students don’t know, they will find out before the test! Teachers forget that the goal is to help the students learn the material BEFORE we assess them!!

So, a student will be essentially be given “baby review” sheets all along and I wouldn’t even limit the questions to just the test questions since many of these students forget everything but if they do one problem each night from a section, it will keep them fresh. How do I complete the square? How do I find the vertex of a quadratic when it is in standard form? How do I solve exponential equations? How do I factor when the leading coefficient is not 1? How do I factor difference of perfect squares? Math asks you to remember a lot!! We need to show kids how to do it! We need to help them be successful. If we can model good study habits, when they go to college, they will use these on their own.

If you are a parent with a struggling student, begin to make up (or hire a tutor) to make up baby review sheets that ask one problem of each type of thing the student should know. When you see they are finally solid on a topic, remove it and just add it back randomly as a check! Good luck!