Posted by A question math teachers answer everyday is “I don’t know how to do this question, can you help?” When working with students in person, a math teacher will often ask followup questions to help understand where a student is having difficulty.
As more and more students are learning online (or asking parents for help with their math homework), recognizing the different ways a student doesn’t know how to do the problem can be very helpful. Further, if students can recognize these ways themselves they can receive better help from their teachers in online forums or online study sessions.
Have you started the problem?
In general, a good starting point is clarifying whether a student
- Has not yet started the problem, or
- Started the problem but got stuck or got the wrong answer.
As an example, consider the following question.
What is the vertex of the parabola \(y=x^2+4x+8\)?
Sample High School Algebra Question
I don’t know where to start!
If a student doesn’t know how to start a problem, start by making sure they understand what the question is asking and all the vocabulary involved. In our example, a student might need to review that the vertex is the top or bottom point of a parabola. In many cases, this might be the push a student needs to feel comfortable getting started on the question.
If a student understands the question, but is still stuck, a discussion of how to approach the problem can be helpful. Ask the student if there are example questions or procedures in the book that can be helpful. Teaching them where to find information they might have forgotten will help them remember in the future.
The vertex of a parabola with equation \(y=ax^2+bx+c\) occurs when \(x = -\frac{b}{2a}\).
One method for finding the vertex of a parabola.
Caution! Most problems can be solved in multiple ways. Try to let the student choose a method they think is best. Further, once basic information is given, let the student try to finish the problem themselves. Even if a big hint is given, a student making the final steps themselves gives them a sense of accomplishment in solving the problem.
I’m Stuck! or I got the wrong answer!
Most times when a student says “I’m stuck” they have actually made good progress on the solution. For example, the vertex of a parabola is a point, so it has an x and a y value.
The vertex of \(y=x^2+4x+8\) occurs when \(x = -\frac{4}{2} = -2\).
One step away from the solution!
Recognizing that the vertex needs both an x and y value, the student can turn their focus towards “How do I find the y value?” A new sub-question can often refocus the student and help them proceed.
For a student who thinks they’ve solved the problem but got the wrong answer, check for mistakes. A wrong answer does not mean all the work is wrong! Calculation mistakes can lead to the wrong answer, but are easy to fix. If a student takes the wrong approach to the problem, they often need to review the definitions and vocabulary. In this case, starting from the beginning again can be useful.
Using that the vertex occurs when \(x=-2\) the y value of the vertex of \(y=x^2+4x+8\) is \[y=(-2)^2+4(-2)+8=4.\]Therefore the vertex is the point \((-2,4)\).
Organizing and sharing your work is helpful! As a student is solving the problem, encourage them to show and explain their work. This will help them review the problem later, but also makes it easier to spot mistakes. (I’ll revisit the power of showing work and multiple methods for solving a problem in an upcoming post!)
Use all your resources to get the help you need!
Regardless of where a student is on a problem, it’s okay to ask for help! Areteem students are always encouraged to ask questions for their online classes using our Online Discussion Forum at classes.areteem.org.
Currently we are inviting all students to use our forums for help, regardless of whether it’s for school math, extracurricular math, or from an Areteem program. Just visit the online forum, create a free account and post your question!
Keep the above thoughts in mind when asking questions! Whether a student is asking their teacher via email, posting in an online discussion forum, or asking their parents for help, clarifying where they are stuck on a problem gives them the best chance of getting useful feedback.
- For more practice problems: Visit our Zoom International Math League site at ziml.areteem.org for free daily problems and other resources.
- For systematic learning: Visit our Online Classes site at classes.areteem.org for live and self-paced online classes and workshops.