TKES Resource For February

Resource: The Joy of X podcast, “John Urschel, From NFL Player to Mathematician.” February 25, 2020.

In this podcast, Steven Strogatz inteviews John Urschel, former NFL player (offensive line for Baltimore Ravens) who retired after three years to pursue a doctorate in mathematics at M.I.T.

The interview begins with early influences in Urschel’s life which prepared him for both a career in mathematics and a career as a football player. His mother played games with him and bought him numerous puzzles and books. She also defended him against a principal who thought he was mentally challenged. (Turns out, he was extremely gifted.) He was also drawn to sports by both peer pressure and his father’s encouragement. This eventually led him to both a career in the NFL and acceptance into MIT’s PhD program.

He then discusses the tension that resulted when he tried to pursue both the NFL and his mathematical education. This tension eventually led him to end his football career so he could focus on mathematics.

After discussing Urshel’s current areas of study, the two finish with suggestions for U.S. math education. Particularly, he discusses the importance of context in instruction. Historically, mathematics was discovered in an attempt to solve real-life problems that people were facing. Too often, this context is removed from instruction. They also discuss racial/gender inequalities in mathematics instruction.

This podcast is an amazing complement to Urschel’s book, Mind and Matter: A Life in Math and Football. (Full disclosure: I was given a free copy of this book by the publisher several months ago.) I believe both the podcast and the book could be useful resources to share with the student-athletes in our mathematics courses. The podcast and the book also provide examples of mathematical problems/ideas that are accessible to many high school students.

This podcast is available on iTunes and Spotify.

This post is in partial fulfillment of my TKES goal for the 2019-2020 school year.

TKES Resource For January

[THOMPSON, C. (2019). Coders: the making of a new tribe and the remaking of the world. NYC, NY: PENGUIN BOOKS.]

In this book, Thompson presents a history of coding, current issues in computer science, and looks forward to future developments in this area. He gives an excellent introductory explanation of coding and investigates the various ways programmers are affecting our professional and personal lives. As someone who has dabbled in computer programming from time to time, I found Thompson’s overview compelling.

Takeaways for educators:

• Thompson does an excellent job of highlighting gender/racial inequities in coding fields. Some of these same issues occur in STEM and must be addressed.
• Thompson’s discussion of current/future advances in coding should affect mathematics education, both in the content and manner in which ideas are presented to students. Open-ended problem-solving activities should be the norm, not the exception.
• There are currently very few formal secondary coding options for students. Thompson’s presentation indicates a rudimentary understanding of coding would be beneficial for most if not all students entering the current work force.
• Thompson’s overview of artificial intelligence/machine learning makes me wonder what the next generation of instructional software will look like. Will students truly receive customized individual instruction in the near future?

 

TKES Resource for December

[Strogatz, S. (2019). Infinite powers. Boston, MA: Houghton Mifflin Harcourt.]

Strogratz intends this book to serve as an overview on calculus for the general public. As such, he concentrates on the historical development of calculus, past and current applications of calculus, and finishes by looking ahead at future technological and mathematical developments related to calculus. He also explains many of the technical aspects of the subject in layman’s terms.

This book is a valuable resource for educators:

1. Infinite Powers supplies teachers with multiple anecdotes, historical facts, and applications which will accentuate classroom instruction.
2. A student taking calculus in high school or college will find the book provides an intuitive understanding of certain concepts that sometimes get lost in an initial exposure to the subject. I personally would consider assigning this book as reading for summer work prior to an AP or Honors course or for extra-credit during such courses.

Related Links:

stevenstrogatz.com

 

Scattered, smothered and…buried?

Last year, one of my AP Stat students sent me an image similar to the following:

Image source

At some point, the subsequent class discussion raised the issue: Is there a relationship between the number of Waffle Houses in a state and the life expectancy of people living in that state? This led to an investigation that I’ve recreated below.

We began by comparing number of Waffle Houses and life expectancy per state:

The small r value was a bit disappointing. However, with a bit of guided questioning, the students soon realized we needed to adjust for number of Waffle Houses per capita. (We eventually settled on Waffle Houses per million residents.)

The r-value of -0.42 was a bit more impressive. After examining the scatterplot and seeing the point on the far right was perhaps an outlier (Waffle House is based in metro-Atlanta, so Georgia has a home-field advantage in number of restaurants.), we removed the data for Georgia and recalculated. r=-0.63! This moderately strong negative relationship was more exciting! As the number of Waffle Houses increases, life expectancy tends to decrease.

Follow-up discussion:

We did NOT conclude eating at Waffle House decreases your life expectancy. Correlation does not imply causation. In general, southeastern states have a lower life expectancy when compared with other regions of the U.S. As stated earlier, Waffle House is based near Atlanta and has spread across the southeast. Perhaps this correlation is merely coincidental.

Comments, questions, and corrections welcomed and appreciated!

Links to source data: retrieved December 15, 2019.

• Number of Waffle Houses per state
• Life Expectancy by state
• State populations
• Excel file with data and charts

 

TKES Article For November

Patterson, Lynne Gannon; Musselman, Meagan; and Rowlett, Joel (2013) “Using the Depth of Knowledge Model to Create High School Mathematics Assessments–RESEARCH,” Kentucky Journal of Excellence in College Teaching and Learning: Vol. 11 , Article 4. Available at: https://encompass.eku.edu/kjectl/vol11/iss2/4

The authors stated their purpose as follows:  “The purpose of this study is to uncover whether teachers know how to use the Depth of Knowledge (DOK) scale to construct high school mathematics assessments. After in-service training on Depth of Knowledge, teachers constructed tests for their midterm exams using the DOK scale. An item analysis of the exams and a teacher survey were used to determine whether the teachers were implementing research through practice and specifically utilizing the DOK scale as they constructed student assessments” (p. 39). After the midterm analyses, the authors concluded that the educators in question did not ask enough questions at the DOK 3 and DOK 4 level. These math instructors tended to underestimate the DOK level of the questions they asked, but even the percentage of the problems they estimated to be at DOK 3 and DOK 4 was well under Webb’s suggestions for those levels.

In my opinion, it may have been a bit unfair to ask teachers to write their midterms at higher cognitive levels. In my own practice, I feel that cumulative exams are more about breadth than depth, and try to reserve higher-level questions for unit tests, quizzes, or projects.

Having said that, I chose this article because of its explanation of the DOK levels. I’m currently trying to focus on: a) correctly identifying the DOK level of a particular math assessment question, and b) writing good questions at the various DOK levels, particularly DOK 3 and DOK 4. The authors do correctly conclude that these issues are a struggle for many teachers, and I’m not sure these are problems that can be solved with a short professional development session.

 

 

 

 

Open-Middle Problems

TKES Webinar for October:

This month, I listened to Robert Kaplinsky’s webinar “Why We Should Reconsider Worksheets (And What We Should Be Doing Instead).“  Kaplinsky argues against traditional worksheets in favor of “open-middle” questions. (See openmiddle.com for examples of these questions. They are organized by topic so you can find ones that match your current class content.)

Kaplinsky claims open-middle questions are preferable for several reasons including:

• They reveal student misconceptions.
• Students enjoy them.
• They require higher-level thinking.

After watching the webinar, I’ve used open-middle problems from Kaplinsky’s site as openers, closers and extra-credit problems with both Precalculus and Technical College Readiness Mathematics (TCRM) students.  The problems work as advertised. Students stay focused on them for an inordinate amount of time. (Funniest comment: “Mr. Mealor, even Google doesn’t know the answer to this one.”)  As Kaplinsky admits, the first time students see these, they do need a bit of encouragement.

I’ve long argued that most students would prefer to work 2-3 challenging problems as opposed to 30 rote, routine problems that are virtually identical. I’m not convinced open-middle problems can totally replace traditional worksheets, but they are a great supplement to class instruction.

Other Kaplinsky resources are located here.

TKES Goal

As part of the TKES requirements for 2019-2020, I set the following goal:

Standard 9: Professionalism

During the 2019-2020 school year, I will participate in a collaborative study (reading one professional article or book a month or listening to one professional podcast/video per month focusing on mathematics, educational practices, and/or professionalism) and incorporate the gained knowledge and perspective into my classroom and school as measured by presenting in group meetings and monthly article/book reflections.

I will document summaries/reflections on this blog.

AP Statistics-Types of Tests Practice

Click here for practice. You will want to make sure that Prediction for a Single y… and ANOVA are unchecked. We haven’t discussed those this year.

Data for AMDM project 3/5/2019

1st period data:

3rd period data:

6th period data:

AMDM Survey 3/4/2019

Go to: mrmealor.wordpress.com

Click here or copy in the following link:

https://goo.gl/forms/I0FCP8Y2tV9PA8Dx2