M.A.T.H. Tips: Vol. 27
Searching for a new book to read on a lazy Sunday afternoon? Check out Amazon for new releases in mathematics! See how math connects to football, art, the secrets of the universe and scientific paradoxes. Here are some new titles you can look forward to reading:
- Mind and Matter: A life in Math and Football by John Urschel: What began as an insatiable appetite for puzzles as a child developed into mastery of the elegant systems and rules of mathematics. By the time John Urschel was 13, he was auditing a college-level Calculus course. But when he joined his high school football team, a new interest began to eclipse the thrill he felt in the classroom.
- Math Art: Truth, Beauty, and Equations by Stephen Ornes: From geometry in motion to the possibilities of pi, this stunning volume reveals how art has been inspired by the beauty and poetry of mathematical principles.
- Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz: From preeminent math personality and author of The Joy of x, a brilliant and endlessly appealing explanation of calculus – how it works and why it makes our lives immeasurably better.
- Paradox: The Nine Greatest Enigmas in Physics by Jim Al-Khalil: Throughout history, scientists have come up with theories and ideas that just don’t seem to make sense, i.e. paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds.
Who says math should stay in the classroom? Try these games to liven up game night with a little math twist!
Though most mathematicians would agree that playing the lottery is not a good investment strategy, a husband-and-wife team found it to be hugely profitable by hauling in almost $27 million. How? They discovered a math error in Cash WinFall, a lottery game run in their home state of Michigan and in Massachusetts.
With odds of just one in 9.6 million, the jackpot in WinFall is almost never won. When the jackpot rose above $2 million, the game would “roll down” smaller prizes to keep the jackpot from swelling. By buying a large enough number of tickets during “roll down” weeks, the couple discovered they were essentially guaranteed to turn a profit and typically won back 15-20% more than what they gambled. Other players, including a group of students from MIT, eventually figured out the odds and began participating in organized lottery games, ultimately making millions of dollars.
Spring semester usually means spring break and distracted students. Whether you are post or pre-spring break, here are a few ideas to reignite the spark in your semester and recapture your student’s attention.
- Find the math in your major. Students often have a hard time recognizing the usefulness of the math they are learning. Group students by major in non-STEM math classes. Have each group identify five ways they use or reference math in a career related to their major. Spend some class time discussing the ways math can be applied by having each group share their results. This can also be used as an online discussion assignment.
- Let the students create the problems. To help students understand how word problems are put together, have them craft their own word problems in class. Provide an outline of the elements of a word problem, including a topic. Let students work in groups. Once each group is finished, collect the word problems and redistribute among the groups. Tell the students not only to try to solve the problem but to identify where the problem could potentially be improved.
- Try the 10-5-5 method of teaching. Lecture no more than 10 minutes before stopping, have students work in groups on a problem for 5 minutes and then discuss the problem as a class for 5 minutes. This method breaks up the lecture and keeps students engaged with the material.
- Stop, break, concept check! Concept check breaks can help students synthesize ideas. Before moving on to the next topic, have students explain to their neighbor the concept just covered, or spare a few moments at the end of class for students to review main ideas with each other. Teaching online? Pick a problem and ask students to write down all the concepts needed to solve the problem step-by-step.
How often have you spoken to a student with a bad test grade and heard “I spent hours” studying? Students often study in ways that don’t translate to retention of material. The research around student study habits indicates that the go-to methods of “read over” and “highlight” fail to effectively prepare students for exams and promote a sense of accomplishment with little actual retention of material.
So, what does work?
Pamela L. Bacon tackles this question in her paper, Effective Studying is a Science, Not an Art: Teaching Students Scientifically-Based Study Techniques. In it she defines best practices for studying and how to incorporate the techniques into the classroom. Bacon also identifies the top methods for material retention as: flashcards, elaborative interrogation, self-test, and spaced out learning. Scientific American published a helpful guide explaining these different learning techniques, which you can find here.
As a math educator, you can incorporate these methods into your classroom with little modification.
1. Give a short quiz on material learned in the previous class. Then provide students the solutions with the needed concepts identified. Or have students write out what they missed based on what concept was misunderstood or lacking.
2. Setup mini self-tests in your homework system. Creating these mini practice tests in an online homework system gives students the opportunity to practice working questions. Students should take these without using their notes to assess their level of knowledge of the material.
3. Have students pick a method from the Scientific American article and commit to using it before the next test. Create an assignment or discussion board to show students’ commitments. After the test, ask students to think about the effectiveness of the method.
4. Divide students into groups and give each group a problem to solve; have them try to solve it without notes. This gives students a chance to discuss ideas, which encourages learning, listening, and identifying areas of deficiency.
For more information, check out The Learning Scientists website.
By: Kelly Jackson
How are my students diverse? Let me count the ways: age, race, ethnicity, language, socio-economic status, sexual orientation, academic preparation, citizenship status. Do they work? Kids at home? If yes, single parent? Do they have a physical limitation? Are they military?
Given the above, how on earth do I begin to teach a class and expect student success? Do I try to be everything to everybody or ignore it all and just teach the syllabus? Is there a comfortable in between? Very early in my career I had an eye-opening experience. I was assigned a self-contained all-deaf section. Before the term a former student, who had failed my class the previous term, asked to enter the section. I warned him of the difficulties that might arise. Did I mention he was blind? So, for each class my lesson needed to be visual enough for a non-hearing student to benefit and my explanations clear enough for a blind student to benefit. It was an awesome lesson for me at an early age!
We all know that our students can bring “baggage.” Some have more than others. Some have people to help them carry the load and others not so much. Here are my top five suggestions for trying to respect the diversity in your classroom and still honor academic standards.
- Have something in every lesson that the lowest-level students can do, BUT also have something that will challenge the highest-level students. Give everyone at least one win and at least one loss. Maybe this comes in the form of warm-up problems or challenge problems. Let them all feel success and failure every day.
- Who know what challenges your students face when they are not in class with you? Make the most of your minutes with them by giving them the most valuable experiences possible in the time you have. Starting late or letting students out early is a disservice to those who need those minutes because they are sometimes the best or only quality time they get with your subject.
- Use technology but don’t abdicate what humans do well. You can help with problem recognition and the common threads that tie topics together. Tech is great for providing students with problems and how to do them correctly. But instructors are great at helping students understand what they did wrong. Let the tech do the busy work, you can do the creative work.
- Math anxiety is real but so is lack of preparation. Keep things in the room comfortable and interactive. That said, students need to be participants in the process. We use the student as a customer model so much in education now . . . well for our product, some assembly is required. Students need to be doing work, interacting with material, and asking and answering questions. Give them an opportunity to interact with the content in class.
- Use examples from a variety of CURRENT fields and interests. Sports, video games, social media, politics, pop culture, science, health and nutrition, etc. Diversify your examples and approaches to each field so every student can feel included, as well as be given an opportunity to understand “the other side.”
Check out these additional resources for addressing diversity in the classroom:
Six Ways Mathematics Instructors Can Support Diversity and Inclusion
Goals for Achieving Diversity in Mathematics Classrooms