An Authentic Task That Models Quadratics

By: Lorraine M. Barron 

Summary of Journal

I had the pleasure of reading this journal article that was written in February of 2015. This article was placing its focus on the Common Core Standard number 4: Modeling with Mathematics. There was a team of teachers that wanted to create an authentic problem situation for their students. They also wanted the problem to fulfill the Common Core Standard for High School math dealing with non-linear functions. The teachers wanted to make sure that the problem was relateable to the students current lives, so they based it off of a school fundraising project that many of the students shared a passion in. The problem had to deal with selling muffins for the fundraiser. The students were placed into groups and then presented with the problem by their teachers. They were then given 90 minutes of work time to figure out the problem and create a visual representation to go along with their findings. The teachers created a very inquiry based learning environment for their students. If the students asked questions the teacher did not give an answer but yet guided them in a different direction by posing more questions for the students to think about. Once the time was up the students were then asked to present their findings to the class and explain what, why and how they did what they did. Once all the groups had presented the teacher followed it up with a closing of the topic. They explained what non-linear graphs are and how they are important to know about. They told the students about maximum and minimums. The last thing the teachers asked the students to do before their time together came to an end, was each student did a quick write. Their version of quick write is each student writes a question that they either still have about the material or a question they have about the material they learned and how it is related to future learning. The very last part of this reading is the teacher's and their self-reflection. They reflect on the on going thought: is it worth spending the extra time with your students to do an inquiry lesson? They then go on to say: yes it is. Throughout their later lessons for this topic they felt that their students really remembered and knew the information better than if they would have presented it in a different manner.  

Reflection of Journal 

I found this journal to be very interesting. I had learned a lot about inquiry skills and how to write an inquiry lesson for science topics, but I had never looked at it from a math standpoint. I really liked that the teachers picked an inquiry based problem that was not only relateable for the students, but also a current issue with their fundraiser. I believe that this allowed the students to be dedicated to finding the answer because they wanted to figure out how to help save their fundraiser in real life. I also really liked that the teachers stated that they picked the problem they did because it can be solved in a variety of different ways. This allowed the student to make sense of the problem in whatever way works best for them and their group members. Another aspect that I really like what that they allowed each group to present their findings to the class. While presenting the students had to explain why they did what they did. The reason I liked this was because when students are able to explain what steps they took and why this demonstrates higher level learning, which is usually closely related to a better retention level as well. I also really liked that the teachers explained how if a group was unable to reach an understanding or conclusion while presenting they would "parking lot" the idea and come back to it later at the end of class. Lastly I never would have thought to do a quick write or an exit slip for math class, but I really liked how they used them. They just asked the students to write a question that was still on their mind about the topic they worked on for the day; all the other quick write I have seen require more that the students write more than one sentence. However for a math lesson that allows the teachers to see how their students feel I think that the way they did the quick writes was perfect. This is something I will use with my future math students someday.