I want to share techniques for teaching math I have not yet covered. During my years of teaching college-level applied math topics and, before that, teaching middle school and high school math topics, I have honed some techniques to support student success. I hope you find something here that supports your teaching and your students’ learning.

Showing work
This is a tough one. Each year it seems more students choose not to show their work when doing their math calculations on homework and assessments. I use a few approaches to encourage them to show their work. As the semester continues, many students realize there is value to it. Here are some of those approaches that help them figure it out:

• At the beginning of the semester, I explain that students may earn partial credit if they show their work. When their answer is wrong and no work is shown, they lose all the points.

• Specifically, I tell them showing work leaves a trail of breadcrumbs that will assist them and the instructor with finding errors. Students often have the correct numbers and calculations written down, but somehow, the wrong answer is the result of their work. Maybe they slipped when inputting numbers and operations on the calculator. It is hard to say. Ultimately, if they have a wrong answer but the correct calculation written down, I give partial credit and that is more credit than if they don’t show their work at all.

• As a follow-up to the previous bullet point, I also explain there are two types of errors – careless and clueless. If students do not show their work and their answer is incorrect, they may think they cannot do the math. This situation supports their frustration and lowers confidence. When work is shown, it is possible to determine whether the error is careless or completely wrong (clueless). Witnessing the moment a student recognizes their mistake is a careless error is quite something. That moment is a perfect blend of frustration in the error and relief they actually do know what they are doing.

Driving analogies
I am a big fan of analogies in many situations and have developed a series of favorites connecting driving a car to learning math concepts. I share these with my students to help them further understand the importance of how they approach their math work since many of them understand and relate to driving.

• Labeling work
  As discussed above, students often do not show their work. Asking them to also label their work with units or descriptions is even more difficult. I tell them that not including units of measure abbreviations with the numbers in their calculations and answers is like driving in a town without street signs. Labeling helps you keep your place when you are doing the math. Many of my students often lose points for not completing problems because they get lost without the labels to help them realize they have more to do or possibly have done something wrong.

• Working together on homework
  It is wonderful when students collaborate on classwork or homework. The learning that happens during these collaborations climbs right up Bloom’s Taxonomy. (If you can teach it, you know it!) Working in groups on homework is one example of this. Another includes working with a tutor or classmate for help. While these are great examples of how our students achieve successful understanding of the concepts, sometimes these collaborations backfire.
  
  I explain to my students when they do math calculations with others, they need to make sure they can do the steps independently without someone guiding them. This is much like being a passenger in a car. Often, we are unsure of the directions to the place we went as a passenger because someone else was steering during our first visit. When we go somewhere we have not been before as a passenger and want to learn how to go there on our own next time, we have to engage in the journey.
  
  I tell students that, similarly, when doing math problems, they must ensure they can do the problem or one like it without guidance. Otherwise, they may not succeed on a quiz or exam when faced with that problem. This is a common situation, and the moment students become aware and engage in fixing this is when they genuinely dig into actively supporting their learning.

• Multiple Paths
  As you already know, I like to teach the Bridge Method (dimensional analysis) when teaching how to convert units of measure. When I initially teach it, I explain it is not the only way to approach conversion, but I find it the most teachable and supportive for students who have very weak math skills when they enter my class.
  
  Most students are dumbfounded when I tell them they can use any method as long as they get the correct answer. Then I explain that it is like driving to a destination. I ask them if they know a shortcut to their school from their home or if there is a way they go to avoid possible traffic, etc. Performing calculations is very similar. There is more than one way to solve most problems, and as long as they get to the correct answer, they are welcome to use it.
  
  Needless to say, I strongly recommend showing their work regardless of their method. I also like to use the driving analogy to tell them it is ok if they perform extra steps to get to their answer. This is like going way out of their way because you do not know the shortcut when heading to shop at the mall. Until they know the shortcut, that is the way they feel comfortable. As they gain confidence and awareness, they become more confident with the shortcut when driving or solving culinary math problems.

• Directions
  Above, when I discussed my breadcrumbs analogy in the Showing work section, that can also be taught using a driving analogy. It is like when we are driving and need directions to help us find our way. If we go the wrong way, we can look back at our printed-out directions or GPS to see where we went wrong. Maybe the directions were correct, but we misread them. We will never know if we cannot see them. Showing work is like providing directions for themselves or someone else to know the path they took.

Supporting our students while they master culinary math topics is challenging. Hopefully, these best practices support your efforts to help your students discover they can master this math and elevate their understanding of numbers along the way!