Inquiry-Based Learning, Collaborative Learning & Homework Videos in AP Calculus

Pratima Kumar, Math Teacher, School of the Arts, Rochester City School District, Rochester NY

All my schooling and college education has been in India. I started teaching Zoology at the local college right after my Master’s Degree in Bio Science. Two years later I moved to New Delhi and found a job as a Biology teacher in a High School. Instruction in India is direct and teacher centered. Classes are big in size but there are hardly any discipline issues due to tremendous respect for teaches and education in general. Resources are limited and there is a considerable amount of student accountability for their learning process.

I came to the US in 1992 and decided to go back to school and get a Teaching Certification in Math and Science followed by a Masters in Computer Science in Michigan. When my kids were old enough to start school full time I decided to join the work force as a HS math teacher at the School of the Arts. Over the years I have come to pride myself as being in one of the best special schools in the RCSD. Our students specialize in one or more fields of arts including drama and Theater, Music, Visual arts, Voice and various instruments.

As part of my professional growth, I am always looking for opportunities to improve my teaching skills and learn new and innovative ways to educate my students.  When I received an invitation to join the Faculty Fellows Program at MCC last fall, I decided to join the group. Looking back I can state with confidence that this was the right decision. In this program I had the opportunity to go through a good amount of literature related to action research, learn from other educators in the program, observe other HS and College classrooms and receive valuable feedback and ideas from colleagues and facilitators throughout the program.

Over the summer, we were required to come up with our individual Inquiry Question for Action Research. With Common core on its way into classrooms all across the state I felt I could work on something that would prepare me as a teacher for the changes coming our way. I was also very impressed with Inquiry Based Learning from one of my previous Professional Development workshops offered by the District. In my reading of the literature, offered by the Faculty fellows program, the benefits of collaborative learning were proven over and over again. When we learned about additional funding that the program would provide us for our classrooms we started to discuss how to use it. This is when the idea of using a pen-cast to put video lessons and HW solution for my students within my action research came in to play.

I have taught AP Calculus AB for several years at SOTA. Most of my AP lessons are direct instruction with the aid of a PowerPoint presentation. I occasionally have my students work with a partner and wrap up the last Marking Period of the year with projects and student presentations every year. I chose to do my action research with this particular group of students with hopes to promote better understanding and in turn prepare them for their AP exam and College instruction in the coming years. My initial Inquiry brief changed a little over time and I added a second question to my Action research before finally coming up with the following.

Inquiry Questions

How does collaborative learning and inquiry based learning impact understanding and application of higher level math concepts in an AP Calculus Classroom?  How does the use of technology for video solution provide my students with Homework help?

Work Plan

All my AP students had me as their math teacher either once or twice through high school. I started the school year, as I always do, with direct instruction with the aid of power-point presentation and Smart board. At the end of the 1st marking period, I informed my students about my involvement with the Faculty Fellows program and my action research. A pre-survey was taken to get some insight into my students’ thought on their preferred learning needs (see attached – Student Survey Pre-Action Research)

I chose a Chapter – Application of Derivatives – in my course with ample opportunities for my students to work in groups. The Chapter was broken into two sections, each running through a little over two and a half weeks. Each section was preceded by a survey and a pretest and culminated with a post survey and a post test. I had a final Post survey upon completion of my action research.

Students received a packet for each section. The packet contained notes, diagrams, problems and workspace. They were put in groups of four and worked through the packet following the steps outlined by the teacher. Each lesson was followed by 2-3 days of practice word problems. Twice a week they received AP questions from old exams as bell work.

Students received homework on a regular basis. Homework assignments were due the following day. I would choose one or more difficult homework problems and put up a video solution on the class website. Students would also receive a worked out solution key either with the HW assignment or on day it was due.

I made changes in my action research based on feedback from the student survey, conversation with students when they came for extra help outside the regular class time, student test scores and ideas and suggestions from colleagues in the Fellows program. I logged my observation and reflections during this time in a journal. This will be discussed further in the paragraphs below.

Inquiry-based learning

As mentioned earlier, all kids in my AP class had me as their math teacher once or twice before and were thus very used to my way of teaching. They had been exposed to Inquiry Based Learning for a brief period of time in their Pre-calculus class with another teacher and reported that they did not have a good experience. I took a pre-survey on preferred choice of instruction before I started the action research (Graph 1a).  Eight out of sixteen students were certain that Inquiry Based Learning does not work for them and another seven were not sure if it would work. I insisted that we give it another try and I promised to create my own handouts to lead them through the process with assistance. Although not very open to the new way of learning, they were very supportive of my action research and offered honest feedback as I progressed. Halfway through my action research, students’ view on inquiry based learning remained the same (Graph 1b). Seven out of fifteen students still did not think that inquiry based learning helps them and another seven were still not sure. Therefore I settled on an approach that was half direct instruction and half collaborative learning. I would do a mini lesson at the start of class and then put them in groups for the rest of the class period. I paid particular attention to the students who had shown a drop in test scores and also shown a dissatisfaction towards this new approach to learning. A comparison of the pre and post students’ survey regarding preferred choice of instruction clearly shows no increase in liking for direct instruction and a slight increase in preference for collaborative learning. (Graph 1)


Graph 1a: Pre Survey Result


Graph 1a: Post-Survey Result

Collaborative learning

I formed groups of four students by having them count one to four as they entered the classroom. Initially this worked for most groups but there was always one group that would get off task and did not finish the assigned work. I continued to form new groups for the next few classes until I found a grouping that worked for all students. I also made sure that each group had at least one strong student who could work through the worksheet and explain the steps to the other students in his/her group. I circulated from one group to another during this time assisting as needed. I made sure to provide individual assistance to those students who still had strong feelings against inquiry based learning and working in groups. From time to time I would throw in some competition among the group – “Let’s see which group gets done with problem #1 first” or “Which group has the right answer?” Why?  After the post survey following the 1st section and student feedback on group size, I changed the group size to 2 on some days and 4 on others depending on the difficulty and number of problems on the worksheet. Some students had indicated that they worked better with a partner than with four other kids in a group.

I also saw a new practice emerge during this time period. A good number of students would come and work on the homework problems during their lunch period in my room. It was rewarding to watch and hear them discuss and explain to one another as they worked through the problems. The test performance for most students improved in the second marking period. (Graph3). I believe this was a direct outcome of Collaborative learning.  When asked to list one positive and one negative outcome of collaborative learning, the student response were as follows:


  • More people to tackle the problem.
  • Teaching others leads to better understanding
  • Learn new strategies, make new connections
  • Opportunity to bounce off ideas and discuss
  • Peers catch mistakes and explain better/differently


  • Getting off track, talking and heading in the wrong direction.

There was a group of shy students who were not involved while working in groups. These students rarely asked questions or took part in discussions. All of them claimed that they learned better when taught directly. Their first test score were very low.  I started seeing some of them outside class for addition help.  It was for the benefit of these few students that I decided to adapt my action research for the second section and go back to direct instruction. They showed some improvement in the second test (Graph 3), perhaps the additional help and direct mini lessons helped. Their interactions within the group setting however remained unchanged.

Homework Video lesson

My first homework video posting on the class website was over a weekend and I was very disappointed to learn that none of the student had watched the video. The next time I posted a lesson I sent the whole class an e-mail reminder.  I made this a regular practice.  More and more students started to go to the website and watched the posted solution. Those who did not watch the video either did not have the time or were able to work out the problem on their own. This was a very gratifying experience both in terms of learning a new technology and also getting positive feedback.  All students in the post survey found the videos to be helpful/somewhat helpful and wanted me to continue this practice.


I used the same test as pretest and posttest before and after each section in the unit. Even though I initially planned on grading the pre-test and using it to see growth, I ended up using it to get a better understanding of the background that the students had for the unit. Were they able to break down the problem? Extract information given in the problem? Draw the diagram and correctly label it? Interpret what was being asked etc.  Most students’ work was satisfactory. The students also got a chance to look at the questions beforehand and get an idea of what was coming next.

I frequently used old AP Questions for bell work and quizzes to expose them to the kind of questions they would see in an Actual AP exam. They also needed practice working within a time frame to complete the problem, for example, students have about two minutes for a multiple choice questions and fifteen minutes for a free response question on the AP exam.  Only a handful of students were able to do these problems successfully on their own. When prompted with a hint or allowed to work with a partner or in their groups of four, more students were able to talk it out and come up with the correct solution. Though this seemed disappointing to me the student still felt confident about their understanding and agreed that they needed more practice with AP questions. (Graph 2)


Graph 2: Response to student survey on Preparedness for AP Exam following practice with AP Questions

Since I used strictly inquiry based learning and collaborative learning in the 1st section of the unit followed by direct instruction and collaborative learning in the 2nd section it was interesting to see if there was any change in test score. (Graph 3)


Graph 3: Student Test Scores for section 1 and 2 during Action Research Unit

Even though most students showed an increase in test score in the second part of the unit there were three students in particular (student # 7, 11 and 14) who scored poorly on the 1st test but showed a tremendous increase in the 2nd test. These were also the same kids who on more than one occasion had expressed a dislike for inquiry based learning and collaborative learning. The increased test score may also be attributed to extra time and effort they put in for the 2nd test to improve their final grade before the end of the MP.

The overall fluctuations in grades in the past three Marking period (I implemented my action research in Marking Period 2), is not very different (graph 4). Some kids showed a drop in grades in the 2nd Marking period but picked up very well in the 3rd. This might not necessarily be due to change in instructional style but also due to the fact that they put in a lot of effort to improve their grades before the mid-session grades are sent to colleges. Our school has a major musical production before Christmas. From past experience, kids participating in the shows show a general drop in grades due to long hours of rehearsals afterschool and several hours over the weekend.  Drop in grades for students # 1 and 4 can most likely be attributed to their participation in the play.


Graph 4: Student Grades for the first three Marking Periods

Going forward  

  • I plan to continue providing students in my AP Calculus class with a worked out solution key along with one or more video solutions as needed. I also plan to use video homework solution for all my other classes – Algebra 2 &Trigonometry and Algebra.
  • I Plan to use Direct instruction along with collaborative for my AP students for the remaining school year.  I will continue to offer individual assistance to students outside class for those who are struggling. Based on the work time in class I will choose group size of two or four.


  • Students have different preferences on what helps them best. It is difficult to use a single approach that can be effective for all of them. As a teacher I think a combination of two or more is desired. The fact that this group of students was at ease with my way of teaching from previous years and was reluctant to embrace something new is understandable and reflective from their feedback. As our district introduces common core curriculum in math next year, I would certainly like to give inquiry based learning another try in my incoming freshman algebra class.
  • Collaborative learning gives students a chance to explain critique and discuss with one another and I think beneficial if they are involved. The students that realized the benefit of working with one another wanted to continue to do that. For those shy students who do not participate, I might have students work on different problems and then explain to one another giving everyone a chance to participate.
  • Video lessons/solutions created by the classroom teacher were well appreciated and approved by all. It allows them go through it at their own pace, rewind and repeat. They also don’t have to wait till the next day to find out how to work out the problem and saved time for me as a teacher as I did not have to redo the homework problem in class. As we move into the 21st century learning, I can see us as educators using not only video solutions but also video lessons for students to review or assist in case of absence. I plan to continue putting video solutions on challenging homework problems for the AP class and extend this practice to other classes as well.


First year Calculus as taught by R.L. Moore, An inquiry based learning approach by Clement E. Flabo

Collaborative learning techniques by Elizabeth F. Barkley, K. Partricia Cross and Claire Howell Major

Calculus by Finney, Demana, Waits and Kennedy

Teacher Action research: Building knowledge Democracies by  Gerald J Pine (2009)

The Reflective Educator’s Guide to Professional development. Coaching inquiry-oriented learning communities by Nancy Fichtman Dana and Diane Yendel Hoppey (2008)

Sample Action research Write-up: A Demo a Day in high School chemistry by Stephen Burgin.


Pratima Student Survey-Pre         PratimaStudent Survey Post       PratimaStudent Survey 4 1 – 4 3          PratimaStudent Survey 4 4 – 4 6