A challenging math class is a veritable rite of passage for students across the world. Working on problem sets late into the night can be frustrating, but most of us who have been through the gauntlet can recall moments of triumph when a particularly tricky concept is understood at last.
Here at AJ, it is the mission of our mathematics departments to make our students’ first engagements with math as enjoyable and rewarding as they can be. In this article, I’ll discuss some wisdom gleaned from working with hundreds of Bay Area math students.
First off, the most critical advice I can give to students is to engage actively with their homework assignments as a means of deepening conceptual understanding and preparing for successful test-taking. Students, parents, and tutors understand that assignments should be completed regularly in order to learn the material effectively. Doing so is essential, but for many students it is ultimately too shallow a level of engagement.
You can read more about our math tutoring approach here.
Students and parents often share that they feel that tests and quizzes do not reflect the difficulty or style of homework problems. Students complete the homework, feel comfortable with the problems, study diligently, yet they walk away from tests feeling blindsided. How can we address this? Here are some tips:
- Complete assignments regularly and on time. There is no substitute for consistent practice, though I will discuss ways to build upon it.
- Be aware of what topics you are responsible for knowing. This might sound obvious, but this information creates a list of goals and objectives that can guide learning and test preparation.
- Think actively about assignments. Teachers assign problems carefully—consider what concepts or skills were tested for each question.
- Create outlines to address critical thinking questions and word problems, especially harder questions. For example, you might categorize the question based on learning objectives or techniques that were required. Take special note of questions that combine multiple concepts.
Students frequently feel that test questions are not representative of homework assignments. There are certainly times where students are tested on their problem solving ability and their improvisational skills. However, more often than not it is that the problems have been disguised or modified so that students need to think while working problems rather than relying on rote memorization. Points #3 and #4 above encourage students to apply metacognition to their learning and preparation.
It can be difficult to implement points #3 and #4 in practice (especially #4). Generally, students should not attempt these tasks until they are capable of solving the associated problems without assistance.
A technique that can help with point #3 is for a student to ask herself, “Why did my teacher assign these questions?” Ideally, a student can look at a homework problem and say, “This question is relevant because. . .” This level of familiarity with questions will improve recall and allow students to work more quickly and efficiently in test scenarios.
Point #4 is trickier, but ultimately once a student can comfortably solve a word problem she can begin to consider which parts of the solution are most important in the context of their current chapter or unit. Be careful not to be overly specific. The goal is not to plan solutions entirely in advance but rather to deconstruct hard problems into easier problems and to look for patterns in our solutions. This task should provide students with a foundation of problems that they can solve while allowing the flexibility to adapt to problems that look different.
The student’s teacher is a great resource because teachers, knowing the exams, can indicate which topics to prioritize. The textbook is also an excellent resource as it will often have categorized questions by topic. Additionally, our tutoring team is an excellent resource because 1-on-1 tutoring is highly effective in demonstrating, in a customized way, how students can categorize questions or how they can develop plans of attack for tougher questions.
AJ can support students and families by modeling the above behaviors in sessions. Our tutors are very experienced and can generally match problems to previously defined categories on the fly. Walking our students through this process will help improve their confidence and their conceptual understanding. We can also help by reminding students that thoughtful engagement with practice material is a long term strategy and will take time to develop.
A final piece of advice for math students new and experienced alike: learn to be comfortable even in the face of uncertainty. It’s easier said than done, of course, but it is an invaluable skill. The strategies listed previously can go a long way.