The paths to "Eureka" moments: Teaching Mathematics in Secondary Education

Archive for the ‘H2’ Category

Functions Bingo!- Just One of Multiple Instructional Strategies

H2- Honor Student Access to Content Material


Teacher-candidates use multiple instructional strategies, including the principles of second language acquisition, to address student academic language ability levels and cultural and linguistic backgrounds.

As a teacher, I use differentiated instructional strategies to target students’ different learning styles. I am also conscious of my academic language when presenting new vocabulary. In introducing new vocabulary, I used the principles of second language acquisition as a guide so as to meet students at different readiness levels.

For the last week we have been working through the algebraic concept of functions. To many of my students, this is a brand new concept. There are many different terms of vocabulary associated with functions and thus care was needed in teaching students this material. First, I had all student copy definitions into their math journals and phrase them in their own words. With each new day, we reviewed these terms through conversation and applied their meanings to new content and perspectives. In this way, I implemented the first of Barcroft’s Five Principles of Effective Second Language Vocabulary Instruction: Present new words frequently and repeatedly in input.

To differentiate the instruction by learning style, I used several different methods of instruction. One of the latest lessons I did consisted of students playing Functions Bingo! A few days ago we had a half day of school and as I was discussing the upcoming day with one of my students and suggesting we play a math game, he offered that we play bingo. As I thought about it, I found that bingo could easily be adapted to be an effective kinesthetic and visual way of reviewing input/output vocabulary associated with functions.

Bingo Functions   3by3 Bingo board

I gave each student the same bingo board (conventionally, in bingo, each person has a different board) and a different function (of the form: f(x)=3+x ). Students were given colored chips to place on their boards. In the front of the room, I had two dice: one red for negative numbers and one green for positive numbers. When I rolled both dice on the document camera, students were asked to determine the sum of the numbers and use the sum as the input of their functions. For example, if I rolled -1 and 3 students needed to determine the sum to be 2 and use it as the value of  in their function f(2)= … if the output of the function, given the specific input, was on their board, they could place a chip on that space. Once one student got a bingo, (three in a row/column/diagonal) I had all students dump their chips of their board and start again with a new function. The first student(s) to get three bingos won candy.

In this way, students were evaluating many functions at different input values through the context of a competitive, kinesthetic and visually stimulating activity. Additionally, with each dice roll, I used the words “Use this input and determine your function’s output, if you put this in, what comes out?” Thus, I frequently used functional vocabulary throughout the game.

Through the game of functions bingo, I have been able to introduce the concept of functions using multiple instructional strategies to meet students of different learning profiles and readiness levels. In the use of a verbal and collaborative game, I have also implemented principles of second language acquisition to address student language ability levels.


Exceptionality in the Classroom

All students can learn. And I believe all students can learn math!



H1 – Honor student diversity and development. 

Attention Deficit Hyperactivity Disorder (ADHD) has become prevalent in the student body. As students struggle through the implications of such a disorder, it is important to recognize the behavioral and academic implications in the classroom. The article below provides some background and commonalities of ADHD as well as trends seen in the development of mathematics skills in students with ADHD.

Math Students and ADHD

Many students seem to find it difficult to transition from elementary addition of positive numbers to the addition of both positive and negative integers. And yet, this is a vital skill to learn. It is my belief that any student can develop the skills necessary and gain understanding of these concepts so as to achieve mastery in integer addition.

One important way to accomplish this is through lesson planning and the implementation of multiple learning styles. I have developed a lesson plan for the teaching visual and kinesthetic learners how to add and subtract with both positive and negative numbers.This is age appropriate for 7th grade students and meets appropriate OSPI standards as described in the lesson.

Teaching positive and negative addition to students with ADHD

Specifically, this lesson was designed with students with Attention Deficit Hyperactivity Disorder (ADHD) in mind. It is a dynamic and active lesson including games and the use of manipulatives to engage the students. In this way, students gain understanding though kinesthetic experience as well as stay engaged through visual reminders. Additionally, the lesson includes a self-monitoring sheet which allows the student to monitor his/her own behavior throughout the activities.  This creates a sense of ownership of the student’s learning which will positively influence future learning. In this lesson, we use colored chips to symbolize positive and negative numbers (as shown in the picture above). This demonstrates visually the differences between positive and negative integers allowing the student to develop a sense of “opposites”.

In writing the above article and designing the lesson plan, I have learned a great deal about the diversity of students with ADHD and how that will affect my teaching. I recognize I will need to integrate engaging activities and learning experiences in my lessons so that students are able to stay engaged. I also recognize the importance of self-monitoring aids that aid the student in developing an ownership of their behavior and learning. Though this lesson was designed for students with ADHD, it could and should be used for a wider demographic of students. It will be important in future lesson planning to consider the class being taught and the individual needs of the students. Additionally, taking advantage of other prompts and manipulatives will be key to presenting concepts to students with different learning styles.