Zach’s Math Strategies

 

Welcome to Part II of our special ‘Academic Coaches Series’ where we highlight our talented Octant Academics team. Today, we introduce you to our go-to for math, Zach Levine. Below, he provides you with some tips and strategies for academic success.

LOOKING FOR MATH HELP?

Zach Levine is a Senior Academic Consultant, coaching students in academics and test preparation. Zach has worked as an educator for over a decade, having started by tutoring his peers while he was in high school. As an undergrad at the University of California, Berkeley, he tutored hundreds of Cal student-athletes in chemistry and mathematics. After graduating, he went on to attend the Graduate School of Education at Cal. While studying the impact of STEM coursework on student-athlete graduation rates, Zach served as a graduate tutor and Assistant Tutorial Coordinator at the Cal Athletic Study Center. In these roles, he developed his skills in academic coaching and traditional coursework support.

Painting a Picture with Math Word Problems

One of students’ most common areas of struggle in any math class is word problems. Students dread seeing a few word problems at the end of a section of homework or at the end of an already stressful test. Word problems tend to make students feel vulnerable and less confident in the work they are doing. So, how should students approach word problems to be the most successful with them?

The best first steps are to draw a picture, where applicable, and assign variables. Nothing is more difficult than trying to do a word problem in your head. I cannot stress enough the importance of having a labeled diagram when doing a word problem. One of the main challenges of a word problem is that the equations you need to solve are not typically given directly to you.

Drawing the problem out and assigning variables helps you keep track of what you are trying to solve for and allows you to write out the necessary equations. Once you understand the problem from a picture and variable standpoint, a word problem is really just like any other problem. You need to ask yourself what techniques you can use to solve the equation(s) you’ve come up with and then try those techniques.

When you find your answer, a smart thing to do is to remember what you were solving for and do a sanity check. If you were solving for the number of apples in a basket and you got -4, for example, you should go back and check your work, because you can’t have negative apples.

One final thing to keep in mind when answering a word problem is units. Teachers are very observant when students don’t include units in their answer, and it leads to students missing points for problems they have otherwise done correctly. Again, check back and remember what you are solving for to help pick the correct units for your answer.

KEY ELEMENTS OF MATH TEST PREP MANY STUDENTS FORGET

You’ve probably experienced your child understanding the material in a given chapter of math but performing poorly on the chapter test. Students often ask me why they can do problems correctly when they are doing homework, but then don’t do as well on the test as they should. One key part of test preparation to keep in mind is studying how to identify the problem types on which to use certain solving strategies.

When students do a given section of homework, that section has specific techniques to use for the exercises given. For example, a geometry section on alternate interior angles will have problems that all involve using the alternate interior angle theorem to complete the problem. However, when the test comes, the problems don’t tell students to use that theorem. The students have to look at it and recognize that the theorem is needed to figure out the question. Studying which elements of a problem signal which techniques to use is a great way to feel confident for using the right solving strategies for test questions.

Another often overlooked part of test preparation is seeking out as many practice problems as possible. Students often get review guides for math tests, work through them, and then take the test. The review guide is a good starting point for studying. If you want to fully prepare for a test, it’s best to search and find more practice problems to challenge yourself. Oftentimes, tests have a question or two that are especially tricky. If students don’t go beyond just the study guide for a test, they may encounter these questions and get stuck on them.

Some beneficial ways to find more practice problems include:

  • Searching the internet for practice problems on a given topic

  • Looking through the textbooks to find more practice problems

  • Reaching out to the teachers in search of more practice

In my first physics course at UC Berkeley, I did 25 practice problems in preparation for a 5-question midterm exam. After doing all this preparation, my confidence was very high and I went into the test and felt like I had seen every problem in one form or another in my studying. I got a 99 on that exam; it was the best I ever performed on a test in college.

  • One more element of test preparation to consider is making an error log as you work through problems. Students tend to make mistakes in groups. As academic coaches, we identify these grouped areas of error and help students fix them. However, students can also make an error log to help them identify their own areas of error. Knowing where you tend to make errors is really helpful for tests because you can keep in mind those tendencies and actively make sure you don’t make those mistakes on the test.

WHY DO I NEED TO SHOW WORK?

Writing down every single step to get to an answer in math often feels like a chore for students, especially ones who feel they can work out the problem in their head. Students often present me with the question “why do I have to show my work?”

There are three main reasons why showing your work in math is incredibly important:

  • It ensures your problem is fully completed

  • It helps reduce errors

  • It can help gain points back on problems you miss

Showing your work is what truly makes a math problem complete. Since math is the application of logic, a worked out math exercise needs to have a coherent and logical flow. I’ve told students to imagine listening to a speech where the speaker gives their opening statement and then immediately delivers their closing line. I ask students how they would react if that happened, and they consistently respond that they would be very confused. I tell them that this is exactly what their math teachers think when they don’t show their work.

Teachers don’t just want to see the correct answer circled on a student’s paper; they want to make sure the thought process used to get to the answer is justified and accurate. In this way, showing your work makes the problem complete.

While it may seem obvious, showing your work also significantly reduces errors in math problems. If our mathematical minds are similar to computers, then our capacity to go through and answer math questions is similar to RAM. When a computer runs low on RAM, it runs slower and less efficiently. The same is true of math students; when they are trying to remember too many things and do a problem in their head, they run slower and are less accurate. Instead of doing the problem in their head, students should write down their work so they can focus on making sure they are doing the problem correctly. They can also go back and check their work later.

The final reason showing your work in math is so important is that it leads to partial credit being given in many circumstances.

Math problems are often characterized as something you either get right or wrong. While that is true, the way points are given out for non-multiple choice math questions is not so simple. If a question is worth 10 points and a student gets the correct answer, they may get 10/10. However, a teacher can easily mark a student off for not showing work. But imagine a 10 point question where a student gets the wrong answer and doesn’t have any work shown. That’s an automatic 0 on that question, because the teacher cannot tell at all what the student was thinking while doing the problem. If, however, a student shows the work that led to their incorrect answer, teachers often award partial credit. Maybe the student made one minor error at the end of the problem, and they end up with a 7 or 8 out of 10 instead of a 0. Showing work can be the difference between small deductions and large deductions in points.

ZACH’S TOP MATH RESOURCES

 
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