Math Education Concepts

Inspiring Motivating Empowering


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Tangible Parting Gifts

I can’t believe the year has gone by so quickly!  It’s already the end of May and there’s only one week left for final exams.  While my time at Salesianum School was short, it will be remembered.  I have memories that will last me a lifetime.

My memories are those that made me laugh, yell, admire, love, and befriend!  Any high school math teacher can relate to the mixed emotions that are experienced in (and out) of the classroom!  It’s not new.  Maybe some day I will share some specifics about those emotions and experiences.

Today, I want to share two tangible gifts I received this year.

1. A t-shirt with my name on the back.  The significance of the t-shirt is that the students labeled me as a teacher who “Keeps it real.”  I gave it to my students straight, no chaser, and they appreciated that.  If they asked questions, I did not sugar coat the answers (whether the questions were about math, friendship, dating, or life).  One of the parents purchased the t-shirts for the entire class (Thank you Mrs. R.).

T-shirt designed by 414-2.

Keepin’ it Real T-shirt designed by 414-2

2. A”K” shaped crepe.  One of my students hosted a French exchange student this year.  Toward the end of the 4th quarter my student earned a 92.2.  He needed a 92.5 to get an “A.”  The exchange student asked me to boost the student’s grade.  I told him I would if he would make me some food using an authentic french recipe.  So they made crepes (the french exchange student used his mother’s recipe – or so he said he did).  It was delicious, so I will deliver on my word.  He was a good student so I would have bumped him .3 points anyway (especially since he missed a few days of school while he was away at France as an American exchange student).

K-shaped crepe made by French Exchange student and his host

K-shaped crepe made by French Exchange student and his host

These are two of the tangible gifts I received this year.  The intangible gifts are too many to name here.  But to name a few I gained friendships, respect, knowledge, love, life-lessons, memories, and so much more.  I will miss my students, but they will always be close in my memories.


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Students Thinking Algebraically

A few days ago I experienced one of the most inspiring moments as an algebra teacher…  I gave my 9th grade students a quiz on solving equations (one-step, two-step, multi-step, literal, etc.).  One of the questions was a word problem that involved buying a season pass ticket to an amusement park versus buying single passes and making multiple visits to the park.  The first part of the question asked students to determine how many trips to the park they would have to make in order for the season pass to be the better deal.  The second part asked the students to write an equation to model the situation.  The third part asked the students to solve the equation.  Most of the students immediately solved the problem by writing and solving an equation.  When they read the second and third parts of the problem they were confused because they had already completed both parts in the beginning.  I was excited!!!!

This is why I was excited…  The students were initially asked to solve the problem using any method (it was an open-ended question).  Most of the students immediately wrote and solved an equation because that was their first thought.  These students were ahead of the test question!  They were already “thinking algebraically” before the question asked them to think algebraically.

After I collected the quizzes the students told me they were confused by the problem and wondered whether they answered it incorrectly.  I told them they answered the question exactly the way they should have.  I told them they were thinking algebraically and that is how they should be thinking.  They were pleased with my response!

The goal of algebra teachers should be to help students think algebraically.  When this happens, students begin to look at problems differently.  They begin to generalize situations and find solutions quickly (and accurately).  Thinking algebraically is a higher level of thinking that most students (and adults) never achieve.  Most of my 9th grade students are already thinking algebraically!  As much as I would like to take full credit for this, I can’t.  Their teachers before me did a phenomenal job and that makes my job easier.


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When Teaching Hurts

Standing in front of the class declaring all the interesting facts about mathematical concepts feels wonderful.  I enjoy math, I enjoy explaining mathematical concepts, and I enjoy watching students as they learn math.

The “hurt” is felt when it’s time to grade exams.  Some students are able to explain mathematical concepts, but have a hard time writing their explanations mathematically.  Some students can solve problems intuitively but cannot write the procedures the way they are taught.  Some students have anxiety attacks at the mere thought of taking a math exam, even when they know the material.

I understand the importance of tests, but I am a fan of assessments (not standardized, but individualized).  Most of my students understand the basic concepts that I teach and can explain them to me during class.  However, during quizzes and exams, those same students perform poorly.  This is when it hurts!  My heart just sinks when I know a student understands a concept, but cannot recall it during an exam.

The ultimate “hurt” happens when it’s time to submit final grades and students just don’t make the grade, so to speak.  My students are really “good” people who are trying to get through college so they can pursue their dreams.  Should one class get in the way?

Of course, the answer is obvious, but there are systems in place.  They are there for a reason, even when we disagree.


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Teacher or Mathematician First?

Earlier this week a close friend, Lawrence, asked me a question.  And for the first time (in a long time) I had to think about the answer.

He asked me if I were a teacher or mathematician first, when I am in the classroom.  I paused for a moment to consider the question.  My first comment was that, since I have yet to earn my PhD, I am not necessarily considered a mathematician.  But I understood his question.  He wanted to know what drives me when in the classroom.  The example he used was that he is an architect first, then an engineer.  His education path is engineering, but his career path is architectural design (or something like that – sorry Lawrence).  But his real joy is designing blue prints for office buildings.  In fact, he is going to design my future institute (a post for another day).

After thinking about the question, I explained to Lawrence that it depended upon the class I taught.  This semester I am teaching a math course for students pursuing degrees in STEM related fields and a math education course for students pursuing education degrees in non-STEM related fields.  My initial answer was “both:  I am a mathematician first in the math class and a teacher first in the education class.”

This was my explanation:

In the math class the students really need to know and understand the concepts in order to proceed to the next math course.  I have to get the math concepts across to the students.  In the education class, the students need to pass a pre-service exam and satisfy this course requirement.  But they are future educators and I want to exemplify what that means to my students.  The goal for each course is different, so I teach each class differently.

My final answer, however, was that I am a mathematician first.  If you put me in a classroom and take away the math I would be less fulfilled.  I decided to teach to share my joy of math and to help others learn and appreciate math the way I do.  I know this will not happen for all of my students, but I want to reach as many as possible.  The classroom is the best place to do this!

So there you have it Lawrence:  I am a mathematician first, teaching is the vehicle I use to express and share my passion for mathematics!


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You Must Always [OR] May Show Your Work

Read this article by David Ginsburg in Education Week: “You Must Always May Show Your Work.”  He wrote about whether or not students should be required to show their work when completing math problems.

This is interesting because I just had this discussion in my class this morning.  My students asked when it is necessary to show their work.  I gave them examples of when it is necessary (open-ended exam problems) and when it is not (when it is a concept not being taught in the course: a concept they should have already learned).

Depending upon the topic/concept I am teaching, it is more beneficial for my students to show their work so they can truly understand why procedures work.  One example is dividing fractions.  If the topic is new, students should get used to working through the procedure (showing work).  When dividing fractions is a concept embedded within another concept (like simplifying complex fractions), then it is not necessary to show the work involved in dividing fractions.  This is just one of many examples.

While I understand both arguments (requiring work and allowing just the answers), there’s a time for both.  In many cases, students can answer questions conceptually, but have difficulty expressing solutions mathematically.  In other cases students are able to memorize answer sets and can recall those answers easily, but do not understand the concepts.  As an instructor, I must use my judgment to make sure my students are prepared for the next course, a certification exam, teaching, or whatever the course is designed to accomplish.

What are thoughts about students showing their work?  Do you require that they show their work or allow just answers?