Instructional Design: Incorporating TPACK

Problem of Practice 

In my classroom, my problem of practice is finding a method or model to utilize in my Response to Intervention Math Lab classes. Currently, my students struggle to stay engaged in both hours of math during the day. As an intervention teacher, I have to both teach the current content, and work to close the gaps, where students are lacking certain skills. I hope to create an environment where students are engaged in both math periods during the day.

I will know that I have achieved this goal based on observable behaviors in my classroom, as well as strengthened confidence. Improved confidence would look like fewer questions on “how to get started” and a greater ability to iterate without taking breaks.


I teach eighth grade math and math lab at a middle school in a suburban school district. My average class size for college prep (regular class) is 28-32 students. We are on a 6-hour schedule, so each period is 55 minutes.

Each grade level (6th-8th) has two math lab courses. I teach both of these classes for the eighth grade, as well as three of the college prep 8 math courses during the day. Math Lab is an intervention course, for students who have historically struggled in the area of math, or who have fallen behind in the curriculum for any reason. Parents, teachers, counselors and administrators work together to decide which students are eligible for this intervention.

These are typically not students who are failing across the board, but rather students who struggle in math (and often science). It is not a course for students who chronically miss assignments, but are capable of work; but rather a course for students who miss assignments because they lack home support, or do not know how to do the math, and therefore cannot complete assignments. Next year, I will have my college prep courses in the morning, and Math Lab in the afternoon. All students in Math Lab will be in one of my college prep hours.

Last year, I struggled to find a Math Lab model that had students engaged in both periods. If I used a pre-teaching model, students thought they could be off-task or disengaged during our college prep class. If I didn’t pre-teach, they would be lost, and therefore a behavior issue during the college prep class, and expect me to re-teach them in Math Lab.

Additionally, last year I taught on a cart, using different teacher’s rooms during their prep hours. Oftentimes these were not math classrooms, and my cart didn’t have room for more than a few calculators and manipulatives. At this time,  I do not know if I will have my own classroom next year. One of the constraints in this situation is that I had no ability to alter the learning space (physical environment) where I am teaching.


In the classroom, I am working with Math Lab students to not only succeed at grade level, but also to build skills they are missing from previous courses. It is important in math that they have skills from lower grades, to be successful in eighth grade. These gaps are primarily in number sense, fractions, integer work, and expressions/equations. Within my problem of practice, I am looking deeper, at not only building these specific skills, but also at building good habits as math students.

I want my students to learn how to ask good questions, and how to advocate for themselves when they are confused. The most important thing that I hope they will build on is problem-solving skills.


I believe problem-solving skills are the x-factor in math, which allow some students to be successful, and cause others to fall behind or miss things. The biggest issue with this, is that in middle school, students are looking for the answer, and are afraid to guess, and get something wrong. The act of problem-solving is uncomfortable, and being wrong isn’t seen as a part of the process, but the end of the process.

My pedagogy in math is that if you “look” at notes or “see” someone do something, you haven’t learned anything. Instead, when you put that into practice, and iterate to find a path that leads to the right answer, you’ve achieved the goal. I also believe that being able to turn around and teach that same concept to someone else is the best way to build confidence in the skill you’ve acquired, it also helps you see the areas in which you are still unclear.

Previously, I have worked with students to learn the material, then had them teach at least one other person once they got it. Students gave feedback that this strategy worked for them, and some even took this idea home and would teach their parents to truly deepen understanding.

To develop the problem-solving piece, I have used task cards, given obscure projects or assignments which require creativity and thought, and I have have introduced game days, where I bring in strategy games that students must play as a team.

I believe what needs refining is my day-to-day work with students to build those problem-solving skills and their number sense. If there was a way to connect those two things, and implement them daily, it would be ideal in teaching these skills that are critical to any struggling math student.


The technology I use is limited, based on a limited circumstance: not being in math classrooms to teach math. I always provide students with pencils, paper, graph paper, and markers. Additionally, in the math lab courses, I use small student-whiteboards to review and practice new skills. This is the favorite activity in lab, because students like that they can answer on their own, with no pressure, and writing on a whiteboard isn’t as final as writing on paper. They don’t worry as much about making mistakes when they can erase easily.

As far as digital technology, I have access to iPads for students, but we typically only use them when we are reviewing and using formative assessment tools like Quizizz, Kahoot! or EDpuzzle. This is an area where I can, and want to improve upon. I believe technology would transform the learning environment in my Math Lab, if I could find apps that allow students to manipulate.

With a lack of physical resources in my current situation, this could open up new possibilities for my students. Additionally, the use of technology to build on that basic number sense could help me significantly, because I do not have an elementary math background.


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