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"It is Easy When You Do It" - Making Passive Algebra Students Active Learners

Kimberly Kinder (Missouri University of Science and Technology, USA)
Session Information
July 8, 2014 - 3:30pm
Teaching & Learning Effectiveness
Areas of Special Interest: 
None of the above
Major Emphasis of Presentation: 
Best Practices
Institutional Level: 
Multiple Levels
Audience Level: 
Session Type: 
Information Session
Plaza Court 2
Session Duration: 
50 Minutes
Information Session 2

Teaching students in College Algebra classes where the success rate is low presents many challenges. I created more student centered learning in college algebra classes.

Extended Abstract

Teaching students in College Algebra classes where the success rate is rather low presents many challenges. I took two college algebra classes and created more student centered learning. Both inside the classroom and outside.

Inside the Classroom:

Student often say, "It is easy when you do it". This statement illustrates the issue of students as passive learners following a well prepared lecture. I believe a student learns by doing, but "doing" homework does not seem to help students develop the depth of understanding that "sticks" beyond the next exam. I took ideas from my years of teaching high school, ideas from blended learning, and ideas from the flipped classroom have begun developing a student centered approach. I have selected topics and concepts that I want be sure that the student understand and had the students work in pairs or group of three. Then I circulated around the room and monitored the progress. I was able to answer questions for small groups. I was able to reassure some students that they were on the right track. I was able to correct errors that I would not have known about if I were lecturing at the front of the class. Students who would not dare ask a question during the lecture were willing to ask in the smaller setting.

One topic that I selected for my alternative approach was rational functions and asymptotes. Students have many misconceptions about asymptotes. They attempt to memorize a list of rules. Often their list is incomplete or incorrect. I created an activity where the students brought a smartphone or tablet with a free graphing application or a graphing calculator and used it to complete a handout. The handout required them to find the domain, degree of the numerator, degree of the denominator and then graph the function using the technology. They then identified the asymptote(s) and recorded them. The goal was to discover the conditions of vertical, horizontal, oblique, and other asymptote by observation rather than by a dictated list. The second day we went over the seventeen functions where I asked guided questions about the relationship of the domain to asymptotes and the relationship of degree of numerator to degree of denominator to the asymptotes. The students were able to "see" the relationship. We also dispelled the myth that a graph cannot cross an asymptote.

Outside the Classroom:

A second part of my experiment stems from the My Math Lab online homework from Pearson Publishing that we have been using for 4 years now. The online homework has an "Ask My Instructor" button which I encourage students to use. I utilize an iPad that I received with a university grant to answer the students' questions. When a student uses the "Ask My Instructor" button, an email is generated containing a link to the problem the student was working. They type a short message explaining their efforts. Responding in a text based email is often difficult and ineffective. I can use the iPad with a whiteboard application to respond with a "just-in-time" video. I use the "Explain Everything" whiteboard application. I am able to record a video where I can write and explain similar to how I would in the classroom or my office. I can upload the video to the cloud then email it to a student or I can post it on "Blackboard".

I view this interaction with my students as extended office hours. A student can email me during the evening while they are doing online homework. Many times I am working late and can respond quickly. I take 5 to 10 minutes to create a video, upload it and attach it to an email. They can view the video, rewind and pause.
Thoughts on my experiment.

I had big ideas of doing activities once or twice a week, but life and teaching other classes got in the way. So I started small. During the first two weeks I took one or two questions and spent the last 10 minutes having the students work in groups of two or three. I would circulate through the class answering questions and giving pointers. In retrospect I am glad that I took this approach. I believe that I gently gained the trust of my students. They were willing to ask questions and willing to be wrong when only 2 or 3 others were in hearing distance. They were eager to have me check whether they had worked the problems correctly. If not I would point them in the right direction and they could correct their mistake. Later I used a review day to give them problems to work in class in small groups. When I used a discovery activity that I had generated, the students trusted that there was a purpose underlying the activity.


I generated a pretest to measure the students' incoming knowledge which I will compare to the final grades. I taught two of four sections of college algebra so I have comparison data for the four sections. I also have data for sections of this course that I taught over the last several semesters. The data for the most recent semester shows that my sections generally had higher averages. Also, compared to prior semesters where I taught the same course, there were generally higher averages also.

Activities in the Workshop:

Participants should bring a smartphone or tablet with a free graphing application or a graphing calculator. Participant will be asked to role play as students during a graphing activity. This will allow them to view how a class might be managed. Then participants will be asked to create a student centered activity that they can take back to their classroom and use.

Final Thoughts

In this day of hundreds of Facebook "friends", students are more socially isolated than ever. They need to know that interacting with other students can be helpful. Also, their instructor is not an unapproachable pillar of knowledge, but rather a human who sincerely wants them to succeed.

Lead Presenter

I have taught at Missouri University of Science and Technology in Rolla, MO for 10 years. I teach College Algebra, Trigonometry, Calculus I and Calculus II. I previously taught high school for 15 years. As a high school teacher I presented many workshops in Missouri. I attended many workshops as well to keep up on the latest trends in mathematics education. I have been working through several university level grants for the past 2 years and I want share my experiences.

I have a husband and two boys. One will be a college freshman and the other will be a high school junior.