M.A.T.H. Tips: Vol. 20

Top Ten Summer School Tips

Summer school offers different set of challenges than during the regular school year; a condensed shorter time frame and perhaps more frequent meetings might be just two of these challenges. Whatever the format, we’ve pulled together ten tips to help make your summer session flow smoothly.

  1. Create a detailed schedule for you and your students. Creating a daily schedule of what will be taught and assignments due helps set expectations and sets students up for success by providing them with a road map for progress.
  2. Identify your core outcomes. It is tempting to try to cover everything in a summer class. However, if you are subject to a reduced time frame, identifying the objectives that can be removed and focusing on the essentials can reduce your and your student’s stress.
  3. Include an initial assessment. Using an initial assessment helps you identify areas where students might need remediation and areas that they might need to simultaneously review.
  4. Remedial assignments. If your course system does not already include remediation, create one or two remediation or review assignments for each unit.
  5. Space assignments out every two to three days. Shorter more frequent assignments help students keep on pace with the course and helps prevent them from falling behind.
  6. Course announcements. Set up course announcements to be sent out to prompt students to stay on track of deadlines.  These can be prepopulated in the LMS and set to appear on specific dates.
  7. Include breaks in long class sessions. Even the best of us need to mental breaks to stay focused.  Include short 5-10-minute breaks in longer class sessions to help students and yourself stay sharp and on task.
  8. Maintain your standards. Summer tempts us and our students to a more relaxed mindset.  Try to maintain continuity with the semester by maintaining your standards for quality work, on time submission of assignments, and attendance.
  9. May the first assignment due as early as possible. Having a first assignment due within the first few days of class aids students in setting the tone and the pace of the course.  Early is also a good time to include a review assignment.
  10. Include supplemental videos. For material that is important and might not be covered in class consider creating or including supplemental videos to support student learning and offer more content.

The “Jigsaw Technique” for Collaborative Learning

There are only so many times you can do Jeopardy and Bingo games to review topics. Plus, these games can be competitive, not collaborative. If you are looking for a way to review and foster collaboration, the jigsaw technique is a good one. The technique dates back to 1971 by Elliot Aronson. It was originally intended to help weaken racial cliques in classrooms. Research showed some success with this goal.

Let’s use Factoring as a sample topic. Suppose you have several techniques you want your students to review for fluency: 5 groups are created (this number can vary). The first will review only factoring out a GCF and factoring out the opposite of the GCF (AKA factoring out a negative), the second factoring by grouping, the third differences of squares and perfect square trinomials, the fourth trinomials with lead coefficient 1, the fifth trinomials with lead coefficient not one. If you do sums and differences of cubes, they can be an additional group or the above can be reworked to accommodate the methods your class focused on. Each group will fill in a prepared handout on their topic. This should include tips for recognizing problems that use the technique and sample problems using the technique. The group members become “experts” at their assigned method.

After an appropriate amount of time, shuffle and reform the groups, placing one “expert” on each aspect of the topic on each team. We now create new 5-member groups with one expert from each previous group. So the new group will have one person who was in group 1, one from group 2, etc. They will now have a new sheet to fill in that includes all methods. With each group having an “expert” to lead the conversation and provide information for each technique.

The jigsaw technique maximizes conversation between several classmates in one activity, since groups switch. The instructor can use care in placing students in expert groups that fit their skill level, to set students up for success when the reconvene with new classmates to function as an expert.

Get started with the basics on this video.




Listen: Helping Students Thrive

Math professor and textbook author Sherri Messersmith joins the Double Shelix podcast to discuss how educators and schools can help students thrive – especially students who arrive in the classroom underprepared for success. Sherri’s teaching philosophy incorporates fun, real-world problem-solving and uses students’ small successes to build their confidence and dispel their math-phobia. Sherri also emphasizes the importance of following your passions and discusses how doing so enabled her career transition from teaching into textbook authorship.

In addition to their interview with Sherri, Double Shelix podcast has a number of episodes on the themes of inclusive STEM, graduate school, women in science, mentorship, and teaching. All episodes can be found on Apple Podcasts, Google Play Music, and DoubleShelix.com.

Alternative Continuing Education and Professional Development Resources

Summer is here and many of us use this time not only to take a break from the rigors of the classroom or administration but also to hone our teaching and other skills.   Organizations such as MAA and AMATYC and NCTYM have archives of webinars and also host summer camps for professional development, but there are other resources that can be utilized to sharpen our craft and just learn for fun.

  • SkillShare, as the name implies, is a platform where by people share skills, although topics tend to be focused on business applications certain topics can be useful in a classroom setting.
    • Requires sign-up and nominal monthly fee
  • Linkedin’s course site. Learning paths range from How to become a photographer, to online learning, to becoming a programmer.
    • Requires sign-in and monthly fee
  • https://www.coursera.org/ is one of the original mooc sites. Courses from a range of school are offered from Caltech and Duke to the University of London. Free and pay for certificate courses are offered.

Don’t miss our Math Career Spotlights where we highlight a variety of careers opportunities and the people behind them.

Watch: Genius Season One, Einstein

Featured on the National Geographic Channel or Blu Ray/DVD

Unless you catch old episodes of Numbers, it isn’t easy to find a good binge-watch with a math spin. New to DVD and Blu Ray and still streaming is the first season of Genius, which focuses on the life of Albert Einstein. Episode one is directed by Ron Howard and the full season is 10 episodes in length.

The series begins with Einstein in 1930’s Germany contemplating a move to the US. He thinks back to his days at Zurich Polytechnic and his meeting of and eventual marriage to Mileva Maric. The early episodes set him up as the genius at physics but bumbler at relationships. He breaks an engagement to another woman, he and Mileva have a child out of wedlock, he later becomes estranged from his other children and Mileva and falls for his cousin, Elsa. There is plenty of family drama! Throughout the series we get to see his thought experiments related to specific and general relativity. His guilt over his part in the furthering of knowledge related to nuclear weapons is also a big plot point in later episodes. His often strained relationships with German scientists also play out throughout the series. The series is accessible to non-STEM viewers, but there are plenty of points where those with a knowledge of math and physics get an even better understanding of his theories and why he is an excellent candidate for the first season of a series on geniuses.

Season two is streaming now and features Picasso and season 3 is in the works focusing on Mary Shelley.


Math News Favorites to Follow

Interesting news sources abound to help you stay current on interesting math news all summer long.  Here’s our list of favorites!

  • Facebook News feeds:
    • Inside Higher Ed
    • Chronicle of Higher Education
    • Mathematical Association of America
    • American Mathematical Society
    • Art of Mathematics
    • Association for Women in Mathematics
  • Math Blogs
  • Twitter
    • NCSM @MathEdLeaders ‏
    • NCTM @NCTM ‏
    • org @mathblogging ‏
    • Math for America @MathforAmerica ‏
    • John Allen Paulos @JohnAllenPaulos ‏
    • Maths History @mathshistory ‏

The Course After-action Report

After any sporting event, major project or implementation teams meet to discuss how the project went, the good and the bad.  It can be helpful to hold a course post mortem or after-action meeting with your teaching team, or just for yourself, to identify areas in which you can improve for the next semester.

When working on an after-action report try to look at the big picture. Begin by identify the goals you wanted to accomplish during the semester. Include not only learning outcomes but any new ideas that you did or did not implement over the semester.  One you have your list of items move on to asking the following series of questions:

  • Start out with a general overview:
    • Identify what went well and what went wrong – try to keep
    • Identify the topics where students succeeded and on what topics student’s struggled
    • Review the exams what went right what went wrong
  • Next go over your lists
    • Review your list of learning outcomes – where the outcomes successful achieved? Why or why not?
    • Review your list of new ideas – Was the implementation successful? Why or why not?
  • Conclude with a summary
    • Identify areas that are successful
    • Identify areas that can be changed for the next semester.
    • List new ideas to try

Summer Reads for Math Lovers

Accessorize your reading list with a new math-inspired beach towel and the most stylish math nerd eyeglasses we have seen!


  1. The Number Devil: A Mathematical Adventure – Hans Magnus Enzensberger, Rotraut Susanne Berner (Illustrator), Michael Henry Heim (Translator), A young boy learns to love mathematics through dreams.
  2. Proof: The Science of Booze – Adam Rogers, Delve into the science behind the production and refinement of alcohol.
  3. Sync – Steven H. Strogatz, The story of the mathematics behind synchronization in systems large and small.
  4. More Math Recs can be found in our other Indexed Posts!

Looking for another way to relax?  Try some mathematical coloring