Journal Summaries #2

Linking LEGO and Algebra

by: S. Asli Ozgun-Koca, Thomas G. Edwards, & Kenneth R. Chelst

(Found in Mathematics Teaching in the Middle School - March 2015, Vol. 20, No. 7)

This was an interesting journal article about an authentic, real-world mathematics situation that was posed on various classes of both 6th and 7th grade students. Under the Common Core State Standards for Mathematics, students should be working frequently to solve and analyze real-world mathematics. By doing this, students should be able to think realistically and allow for flexibility in their solving. In many cases, it is up to teachers to create these authentic math situations for students to work with. It is suggested that authentic learning have real-world connections, use a large amount of time and a vast amount of knowledge, utilize multiple viewpoints of the problem, allow for extensive group work, and require students to find a solution but also analyze that solution.

The activity described in this article was called the LEGO Pets Activity. The 6th and 7th grade students were asked to create dogs and ducks out of a set amount of LEGO pieces. The first part of the activity began by asking students to do this using 6 large and 13 small LEGO bricks. Students worked on some trial and error, and recorded the various combinations they came up with. During this, class discussions were held regarding how the students could work to create the most efficient and profitable amount of animals, using the pieces provided. It was decided that the most profitable combination of LEGO animals, given the amount of materials, would be achieved by building two ducks and one dog. Using an equation, students found that this would surmount to $57 in profit for the LEGO company. Students were then asked what would happen if they were given one additional large or small LEGO brick. Discussion occurred regarding this idea, and most students believed this would not have very large of an effect on profits.

Part 2 of this activity had students working with a larger number of materials. This time, they were asked to create more ducks and dogs, instead using 16 large bricks and 31 small. Students quickly realized this was going to require more work, so took the option of using a spreadsheet over creating the animals by hand. They were introduced to the spreadsheet and some various functions, and learned about the formulas within. Students also worked again to figure out the most profitable combination of animals. It was found that with these materials, four ducks and three dogs profited the most for LEGO at $135. At the end of the article, it was noted that the use of technology in this activity really promoted student learning. In addition, the activity was both authentic and made use of modeling. It was a very real-world activity by having students work with LEGO's and think in terms of efficiency and profit.

I thought this was an interesting article overall. The idea is good with the use of LEGO's and having the students think in terms of being efficient and also generating the largest possible profit. I also liked the idea of using the spreadsheet. However, if students did not have practice with a spreadsheet or understand the purpose of one, I think it would be pointless to present. I do not know the background knowledge of the classes this activity was done with, but I would definitely want to make sure students understood how to use spreadsheets before having them work with one. I do not think that I would implement this problem in my classroom, because I will not be teaching middle school mathematics. This would be too advanced for an elementary school classroom. However, if done correctly, I think this would work well and allow for a lot of student inquiry in a middle school mathematics classroom.

STEM Gives Meaning to Mathematics

by: Lukas J. Hefty

(Found in Teaching Children Mathematics - March 2015, Vol. 21, No. 7)

Both the NCTM Process Standards and the Common Core Standards for Mathematical Practice work together to emphasize the importance of students actually taking meaning away from mathematics. Simply memorizing content is not the basis of mathematical knowledge anymore. The school featured in this journal article was called Douglas L. Jamerson Jr. Elementary School, and their focus was to promote the use of engineering activities to involve real-world mathematics in the classroom. The teachers at this school collectively worked for multiple years to develop activities for each grade level that combined math and science concepts into engineering projects. School wide, the overall process for each project involves planning, designing, checking, and sharing. 

One example of an engineering project described in the article was rubber-band powered vehicles made of K'Nex. Students would do a variety of mathematics during this project, in addition to constructing via blueprint plans, measuring, investigating and experimenting, recording and analyzing data, and participating in class discussions. The goal for this project was for students to create the most efficient car to go a certain distance. 

Teachers at this school noted that they saw little frustration in students while working on the engineering projects. They also explained that when doing these projects, they still have a daily period of mathematics instruction in each individual classroom. Students then utilize what they are learning in math while working on their engineering projects. In addition, the teachers look to build upon student's prior math knowledge from previous grades. The implementation of these engineering projects have made some remarkable changes in the achievements of the students at this school. Teachers noted that students were better able to problem solve, think more critically, and apply mathematics to the real-world and to their own lives. The school also noted that they have seen pretty drastic changes in their student's math and science scores on standardized tests. Some suggestions were additionally given for teachers or schools interested in starting a similar program. They suggested that a good starting point would be to investigate simple ways to integrate mathematics into other subject areas. Then, group collaboration is highly beneficial in order to implement this type of program.

The idea of involving engineering projects that utilize mathematics and science is a great idea. However, I feel that this would be extremely time consuming. Most schools that I have observed in are very caught up in standardized testing. Therefore, they focus mostly on content rather than application of hands-on activities. While I do believe that these types of projects are very interesting and beneficial to students, I do not know how realistic they are to implement in a regular school schedule. Adding another block of time each day for engineering projects may be very difficult to squeeze in. I am not saying that I am against this type of school work, because that is certainly not the case. I think that authentic, project-based learning is highly beneficial to students. They take away so much more meaning from these types of activities. I just believe that this type of curriculum would be challenging to implement, unless drastic, school or district wide changes in the curriculum were made to allow for engineering projects like the ones described in this article.

References:

Hefty, L. J. (2015). STEM gives meaning to mathematics. Teaching Children Mathematics, 21(7).

Ozgun-Koca, S. A., Edwards, T. G., Chelst, K. R. (2015). Linking LEGO and algebra. Mathematics Teaching in the Middle School. 20(7).