M.A.T.H. Tips: Vol. 13

Post-Exam Training:  How to Learn from your Mistakes on the First Exam

We often focus on test-taking skills for before and during a test, but neglect the “after.” Students would benefit from some help understanding how they can learn from their mistakes.  The first key skill is identifying the types of mistakes they make, only then can they work to correct them moving forward. In math there are four basic types of mistakes:

  1. SECRETARIAL: copying the problem down wrong, misreading sloppy handwriting between steps
  2. COMPUTATIONAL: arithmetic mistakes
  3. PROCEDURAL: generally understanding the problem but mixing up or missing a step, (as an example, not completely simplifying an otherwise correct answer)
  4. CONCEPTUAL: wrong procedure or left blank

The first two are typically “in test” fixes. A student may be working too fast, not checking their work, or suffering from anxiety. The third and fourth are preparation issues. A student making these mistakes at exam time is just not fluent enough with the material.

After a test, students can check to see what type of mistakes they have made and see if there are any patterns, then they can implement those great “before” and “during” strategies.

Another strategy from reader Virgil Gibson at Harrisburg Area Community College:  “One practice I’ve implemented in my classes is dividing the class into working groups of about four students and have them collaboratively identify the reasons for any incorrect or incomplete responses to problems on each others’ papers. They learn while teaching each other.”


Meet our M.A.T.H. Tips Faculty Advisors!

SuzannSuzanne_Galaydae Galayda, Lecturer at Arizona State University

I’ve been teaching 13 years. I typically teach College Algebra, Precalc, Calc and Statistics. This semester I am helping out with Physics!  I wish someone had told me that teaching math is part being an instructor, and part being a therapist– a large part of my job is emotional coaching, especially freshman.  To stay sane I hang out with my three cats and do yoga.





Dr. Kelly Jackson, Camden County College, NJ

I began teaching as a full time faculty member in 1992, focusing primarily on developmental mathematics and non-STEM college level courses. The biggest change I’ve noticed in students in that time is their current reluctance to persist, struggle, and productively fail. I wish someone had told me how important being a source a motivation would be in my job. My hobbies include reading, beekeeping, and cheering on the Phillies.

Math Career Spotlight: Steven Coates, Professional Services Engineer

Welcome to a new feature on Tips N Tricks that features people from a variety of careers who started off studying mathematics.

Our first Math Career spotlight, we’d like to introduce you to Professional Services Engineer, Steven Coates.

“I am a Professional Services Engineer with Fortinet, a network and security company. I provide design, implementation and configuration services to customers for network security, routing, switching and access.

How do you use math or mathematical problem solving in your work? How does your math background help you in your job?

A large part of my job is troubleshooting and problem solving. With IP networks, you must take logical steps in problem solving. The rigor required for success in mathematics directly translates to quickly and efficiently dealing with complex network issues.Also, IP networking requires a thorough understanding of the binary number system.

What motivated you to study math?

I initially started my college career in the Electrical Engineering track. As I was a non-traditional student, I didn’t start college until I was 29, I had to start in lower level classes. In order to take EE classes I needed to have completed Calculus 1. My first college math class was College Algebra in the fall of 1999. By the following fall, I had passed [all the prerequisite courses and Calculus]. At this point I was still a EE student but was not very interested in the engineering classes. Within a couple of semesters I changed my major to Math and never looked back. There was just something about Math that grabbed me.

What would you say to a student who is thinking about studying math but doesn’t what a typical math career.

A degree in math is very attractive to employers in just about any technical field. The problem-solving skills and the logical thinking required makes someone with a math degree a great asset. If math is interesting to you, study math.”

Lo-res_185329426-SIf you know someone who would be ideal to do career spotlight, submit their name to us!

Watch: Gifted, Movie Review

Video_clipTrailer : https://www.youtube.com/watch?v=1J8cd8QSLkc

IMDB: http://www.imdb.com/title/tt4481414/

The IMDB Description for Gifted: Frank Adler (Chris Evans) is a single man raising a child prodigy – his spirited young niece Mary (Mckenna Grace) in a coastal town in Florida. Frank’s plans for a normal school life for Mary are foiled when the seven-year-old’s mathematical abilities come to the attention of Frank’s formidable mother Evelyn (Lindsay Duncan) whose plans for her granddaughter threaten to separate Frank and Mary. Octavia Spencer plays Roberta, Frank and Mary’s landlady and best friend. Jenny Slate is Mary’s teacher, Bonnie, a young woman whose concern for her student develops into a connection with her uncle as well.

A few comments: The movie is intended to pull heart strings and focuses more on relationships than the mathematical proof  that is part of a subplot. The Navier-Stokes problem mentioned in the movie is one of seven Millennium Prize problems in mathematics. The Clay Mathematics Institute offered a US $1,000,000 prize to the first person providing a solution for each problem. The problem featured deals with equations which govern the flow of fluids such as water and air.

One scene in the movie harkens back to a scene in the children’s classic Matilda, in which the young girl mentally multiplies 379 and 13. Her teacher scratches out the work on paper to confirm her answer.  https://www.youtube.com/watch?v=QdDlB7Ky8Ns

In a nearly identical scene in Gifted, the teacher reaches for a calculator to check the youngster’s computation. Does this say something about how elementary teachers are prepared now?

Looking for additional math-favorite movie recs, TV shows and featured video clips, check out our Index and Select “Watch”.

Course Spotlight:  College Algebra Unexpected Unknowns

College Algebra has a reputation of being that math class that every college freshman needs to take. And in truth many freshman do take College Algebra whether on their way to another math course or as a terminal degree requirement.  No matter who is in your course there are three unexpected areas of difficulty almost all students have.

  1. Operations on Fractions – Even the best students balk when it comes to hand manipulation of fractions. The key to getting students past this hurdle is familiarity. Include fraction review in the beginning of the course and then liberally use fractions in other problems.
  2. Interpreting slope – When you ask a student to tell you what slope means most parrot “Rise over Run” but ask them to state the meaning of slope in context in a sentence and be prepared for blank looks.  Help your students understand that slope measures rate by including interpretation questions in your problem sets.
  3. Close reading – Students are trained to find keywords that they think can help them solve problems.  By focusing only on what they think are key words and numbers students miss important details in word problems such as the need to convert units, which variable is independent and whether the answer makes sense. Help students learn to close read by including scaffolding problems that break down questions into parts and lead students through the steps of close reading and problem solving.

Course Spotlight: Statistics and Liberal Arts Math

Statistics_Data_StudentsLo-res_158698271-STeaching Stat or non-STEM math? Want to give your students some real (and up-to- date) data to analyze? Try some of these sites.

World Data: population, life expectancy, climate, etc.







Careers: job growth/decline, earning potential






College info: majors, college degrees, completion rates, cost, earnings







Read: Mathematician’s Shiva

IS098QY3FPublisher’s description of Mathematician’s Shiva

Alexander “Sasha” Karnokovitch and his family would like to mourn the passing of his mother, Rachela, with modesty and dignity. But Rachela, a famous Polish émigré mathematician and professor at the University of Wisconsin, is rumored to have solved the million-dollar, Navier-Stokes Millennium Prize problem. Rumor also has it that she spitefully took the solution to her grave. To Sasha’s chagrin, a ragtag group of socially challenged mathematicians arrives in Madison and crashes the shiva, vowing to do whatever it takes to find the solution — even if it means prying up the floorboards for Rachela’s notes.

A few comments:

I found this book delightful. It had quirky characters that felt familiar. If you enjoyed Julie Schumacher’s Dear Committee Members, you’ll enjoy this (if you have not read that book DROP EVERYTHING AND READ IT NOW). You will catch yourself with a goofy grin or just laughing out loud at many scenes. There is an authenticity in the depiction of academic life that will ring true. Quick read.

  • A great interview with Rebecca Goldin on why math is the best way to make sense of the world http://bit.ly/2gYZzEQ
  • The internet in a short amount of time is now an integral part of our lives. In this older article from Ars Technica UK you get a walk through of what goes into making our interconnected world. http://bit.ly/2xNF0oe
  • Looking for additional book or article recs from our Math Advisors?  Visit our Index and Select “Read”.