Walking into a math class can often inspire dread or fear in students. However, when students walk out of Department of Mathematics‘ instructor Ms. Josephine (Jo) Johansen’s Fundamental Math Systems, Introduction to Mathematical Thought, or Numbers and Beyond courses, they walk out smiling. The Rutgers-Camden alumna specializes in developing presentations of mathematical concepts to mathematically phobic students. Based on her receipt of the EOF Champion Award, which is given by the New Jersey Department of Higher Education for work with the Educational Opportunity Fund (EOF) Program, and the Provost’s Teaching Excellence Award, both in 2001, and the overwhelming support of her students, it’s clear that Ms. Johansen has been very successful in her endeavor.
Ms. Johansen’s interest in math developed at a young age, when her sixth grade teacher presented the class with a challenging math riddle. Ms. Johansen was the only student able to solve the problem. Seeing mathematical problems as puzzles to solve opened her eyes to math’s potential, and she was hooked.
Despite her now-obvious talent for teaching, Ms. Johansen initially was not interested in that career path. In college, she contemplated engineering as a career, but after learning about the hazards engineers endure, she changed her focus, briefly toying with the idea of entering the computer science field. Her advisor recommended she consider becoming a teacher, and while she still did not feel that teaching was the job for her, she decided to get her teaching certification as a back-up plan. Ms. Johansen student taught at Camden High School, and, much to her surprise, found she genuinely enjoyed helping students understand mathematical concepts. The excitement and happiness she felt seeing students who previously struggled with a concept begin to understand “the beauty of math” confirmed for Ms. Johansen that she was meant to teach.
A year and half after her graduation from Rutgers-Camden, after taking time off to have her first child, Ms. Johansen returned to teach at Camden High for two years, followed by two years at Camden County Vocational School, and six years at Camden County College. In Fall 1989 was hired as a full-time instructor by her alma mater. Due to budget issues in Spring 1990, she was laid off, but was quickly rehired, in part because of the barrage of students’ objections. Even after a few semesters, her approach to teaching math was legendary, and the students were reluctant to lose her.
Seeing a constant flow of students who are fearful of math made Ms. Johansen realize that regurgitation is not an ideal way to teach mathematical concepts. Instead, she comes up with analogies relative to math that enable students to actually understand the material. One of her examples is regarding the algebraic commutative property A+B = B+A. In order to understand that the commutative property is about the order in which the elements are chosen under some action, and whether the action is order sensitive or not, Ms. Johansen tells her students to think about putting on your hat and coat versus putting on your socks and shoes. You can put your hat and coat on in any order and the outcome is the same. However, putting your socks and shoes on is order sensitive, and the outcome is different if you try to reverse the order. Addition and multiplication have freedom in their order, and so are the hat and coat, while for subtraction and division, order does matter, and so they are the socks and shoes. As Ms. Johansen says, “these types of insights begin to dissolve the fear of math.” Her method has worked well; after learning about this new way of thinking, “students tell me though they have never liked math, they now have an appreciation for its usefulness. This, for me, is the biggest reward,” she says.
Ms. Johansen’s approach has extended outside of the classroom, and she is active in math textbook publication. She was recently part of the writing of the recent Elementary and Intermediate Algebra Combined Approach, published by Cengage Learning, and is currently completing a book to be used in Fundamental Math Systems I and II. In the textbooks, she uses poetry (see below for an example of her poetry) to explain her analogies. Ms. Johansen explains that she has always enjoyed writing poetry, partially because it’s mathematical in structure. She has written limericks about a multitude of mathematical concepts for students at every grade level, giving them another way of understanding a concept and showing them how math can be applied to every day events.
Despite her initial reluctance to enter the education field, Ms. Johansen is so glad that her career has been spent in the classroom. “I have enjoyed teaching every semester from the beginning of my career and cannot imagine retiring. The students are interesting and I truly enjoy breaking the bonds of math phobia.” The students of Rutgers-Camden are equally as lucky and appreciative of their gifted and committed instructor.
The following poem describes Ms. Johansen’s philosophy relative to the teaching of mathematics:
Math Dust
Formula regurgitation
Explains why this nation
Is mathematically deficient
A child learns what they need
To temporarily succeed
Passing the test seems sufficient.
Somehow mathematics
Moves to the attics
Of many people’s intellects
In boxes separated
By walls corrugated
Soon the dust collects.
However it is my belief
This achievement is brief
It feeds the mind for a short time
To never accept
Any empty concept
Is the purpose for my rhyme.
When the commutative property
Is seen as A+B=B+A expressly
It is unclear that order is the issue
Like putting on your hat and coat
The order, please note
Is immaterial to you.
Addition enjoys this freedom
So too, in a multiplication kingdom
But some actions have order issues
When considering subtraction
Or the division action
These put on socks and shoes.
When taught to memorize
Math fails to mesmerize
Giving the answer for a day
If shown the connections
With its true directions
One can solve come what may.
About Josephine Johansen
Rank: Instructor of Math
Hometown: Voorhees, NJ