{"id":127523,"date":"2023-11-20T13:57:10","date_gmt":"2023-11-20T19:57:10","guid":{"rendered":"https:\/\/uwm.edu\/news\/?p=127523"},"modified":"2023-11-27T10:39:13","modified_gmt":"2023-11-27T16:39:13","slug":"exploding-dots-help-teach-students-about-math","status":"publish","type":"post","link":"https:\/\/uwm.edu\/news\/exploding-dots-help-teach-students-about-math\/","title":{"rendered":"\u2018Exploding dots\u2019 help teach students about math"},"content":{"rendered":"

Nick Johnson liked mathematics only \u201ca little bit\u201d in high school and didn\u2019t think he was cut out for college. \u201cI never saw myself going to college. My parents didn\u2019t go to college, and we just never had the money.\u201d His last high school mathematics class, pre-calculus, was in 1999, and he dropped it because \u201cI couldn\u2019t understand anything, and I didn\u2019t need it for graduation.\u201d<\/p>\n

That\u2019s changed, thanks largely to the concept of exploding dots.<\/p>\n

Johnson, who is a math specialist in the College of General Studies\u2019 First Year Bridge program, recently gave a presentation on the topic of exploding dots at the National Council of Teachers of Mathematics in Washington, D.C. \u201cIt\u2019s the Super Bowl of mathematics education,\u201d he said.<\/p>\n

\"\"
The “exploding dots” concept helps students grasp the concept of place value. (UWM Photo\/Troye Fox)<\/figcaption><\/figure>\n

In his current role as a math specialist, he is helping other students on their journeys to understanding and enjoying mathematics.<\/p>\n

The bridge program provides help to students whose math skills aren\u2019t quite up to college level yet, giving them the support they need. Students also work with a self-paced online program called ALEKS.<\/p>\n

Johnson\u2019s own journey to becoming an instructor gives him an understanding of ways to reach his students. He believes when students see mathematics as approachable and enjoyable, their confidence greatly increases and their understanding of mathematical concepts and ideas soars.<\/p>\n

After suffering an injury while working at a printing company a few years out of high school, he decided to change his career path. \u201cI was out to dinner with my wife and said, \u2018Maybe I\u2019ll finally go to college. I kind of like math a little bit.\u2019\u201d<\/p>\n

He started in the bachelor\u2019s program in mathematics education at UWM. At the same time, he began educating himself about the field of mathematics, going to the library and searching the internet.<\/p>\n

\u201cI remember going to the library and getting this book, \u2018Pre-calculus Demystified.\u2019 I was teaching myself and found some stuff online.\u201d<\/p>\n

How it works<\/h3>\n

Along the way, he discovered the concept of \u201cexploding dots,\u201d championed by mathematicians James Tanton and Sunil Singh, who were involved with the Global Math project<\/a>\u00a0. Exploding dots uses a visual approach involving boxes and dots to show how mathematics, particularly place value, works. Students put a dot in a box, and when they add another dot representing a certain number, the dots explode and go into a box to the left, representing a different grouping. Sound effects contribute to making the mathematics playful and fun.<\/p>\n

A blog on exploding dots<\/a> explains the idea in terms of counting coins. If a student has 12 dimes and 12 pennies, the 12 pennies can be dots in the far right hand side box. The pennies can then be exploded into the next box on the left to make another dime, leaving two pennies in the first box. Ten of the dimes can then be exploded into the next box on the left, making $1, leaving 3 dimes, and making a total of $1.32.<\/p>\n

This example uses base 10, but exploding dots can be used with other bases, including base 2, which is helpful in working with computers. The concept can also be used in higher levels of math, ranging from long division to working with polynomials in high school and college-level courses, according to Johnson. Advanced algebra with polynomials is no different nor harder than grade school arithmetic, Johnson said.<\/p>\n

After completing his bachelor\u2019s degree in math education, Johnson decided he might not want to be a high school teacher, but he did enjoy tutoring. He decided to focus on mathematics for his master\u2019s degree at UWM. He continued exploring the ideas behind the exploding dots in his thesis, titled \u201cExploring the Division Algorithm in Euclidean Domains with Exploding Dots.\u201d<\/p>\n

Johnson has now been working with students in the bridge program for four semesters. He has given presentations on exploding dots to a number of regional mathematics conferences, and sent a proposal for a talk on the topic to the math teachers council in the spring. He\u2019s thrilled that it was accepted, and that he got to present in D.C.<\/p>\n

Meeting his math heroes<\/h3>\n

Along the way, he\u2019s had a chance to meet his math heroes Tanton, \u201cthe main dude behind exploding dots,\u201d and Singh. He also has a collection of mathematics T-shirts, including one that reads \u201c17 is a palindrome in base one-and-a-half.\u201d<\/p>\n

His goal is to help his students move from noncredit math courses to credit courses and beyond with a better understanding of the way mathematics works, said Johnson. \u201cI can relate. I know what it\u2019s like to sit in a math class and have no clue what\u2019s going on.\u201d<\/p>\n

One of the challenges in his classes, he said, is reaching out to students who\u2019ve had bad experiences with math or find it boring.<\/p>\n

\u201cAny subject, if you enjoy learning it, you\u2019re going to do well. My main focus is to get every student to believe that they can do math, that they can enjoy learning math. It\u2019s not going to be an awful struggle.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"

Nick Johnson once dropped out of math class in high school. Now, as a UWM math specialist, he helps incoming college students get up to speed and conveys his love of the field. <\/p>\n","protected":false},"author":835,"featured_media":127530,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","uwm_wg_additional_authors":[]},"categories":[174],"tags":[],"section":[139],"display_categories":[115,116],"related-coverage":[],"uwmnews-feed":[],"class_list":["post-127523","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","section-science-technology","display_categories-top-story-secondary","display_categories-top-story-section"],"yoast_head":"\n\u2018Exploding dots\u2019 help teach students about math<\/title>\n<meta name=\"description\" content=\"Nick Johnson once dropped out of math class in high school. 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