Part 4 of 4: Success in Different Forms
This is the final article in our 4-part series investigating math in LEGO Robotics Competitions. Part 1 introduced the past research and the context of the present investigation — a local LEGO robotics competition where investigators conducted interviews about team strategies. Part 2 laid out the range of strategies that were observed, and teased out an interesting result that teams using math-based strategies seemed to have widely varying success in the competition, with math-users both leading the pack and trailing at the rear. Part 3 looked in depth at the winning team and found that purposeful use of mathematics was central in both their programming and overall planning strategies.
But what about the teams that used math, but still scored low? Would it have been better for them to choose a non-math-based strategy?
Focus Team Surveys
As mentioned in the previous article in the series, the research team met with four Focus Teams outside of the competition, hoping to gain greater insight into their solution strategies and what they got out of participating in the competition. Each of the four Focus Teams completed two surveys before the competition, and the same two surveys again after the competition. The first survey consisted of 12 test-like questions that asked the students to solve problems involving robot motion (e.g., how many motor rotations are required to make this robot move this distance?). The second survey, however, measured students' attitudes towards robotics and mathematics, including questions about their level of interest in robots and math and also their view of how valuable math is for doing robotics.
Who were the Focus Teams?
Two of the Focus Teams consisted of students from elementary grades, and are codenamed Team E1 and Team E2. The other two consisted of middle school age students, and are identified as Team M1 and Team M2. Table 1 shows the teams, their grade levels, the number of students on their team, the strategy the team used for their first move, and their rank and best score from the competition.
Perhaps not surprisingly, the middle school age teams outperformed the elementary school age teams in the competition as evidenced by their much higher ranks and final scores. This is not a universal effect, however, as there were a number of elementary school age teams who did do very well in the competition (ranked #5, #7, #9, & #12 out of 22 teams). Unfortunately none of those teams were Focus Teams, and so did not take the surveys.
Among the Focus Teams, two (Teams E2 & M2) used the math-based Calculate-Test-Adjust strategy for their first move, and the other two teams (Teams E1 & M1) used a non-math-based strategy. This provides a nice contrast to explore the effect of using math in a team's solution. The conclusion from Part 2 does still standout – using a math-based strategy leads to high competition scores in some cases (Team M2), but not in others (Team E2).
But there may be more to tell about the teams than just their competition scores. What about the surveys?
The Learning Benefits of Using a Math-Based Strategy
Figure 1 shows the results from the robot math knowledge survey administered to the Focus Teams. The middle school age teams (Teams M1 & M2) have higher scores overall than the elementary school age teams (Teams E1 & E2), which is not surprising. The older students have more experience with mathematics in general, and it shows when they solve formal problems that make use of math.
However, a more interesting pattern can be found by looking not just at the scores, but at the gains. The two teams that used the math-based Calculate-Test-Adjust strategy (Teams E2 & M2) both improved on their survey scores from the beginning of the competition to after, but the teams who used a non-math-based strategy (Teams E1 & M1) did not. This suggests that regardless of a team's initial level, using math in an explicit way in the competition solution improves student use of math when solving more general problems relating to robot movements.
If increasing students' problem solving abilities using math is a goal of the robotics team, then just attempting to use a math-based strategy may have real advantages, regardless of how it impacts the team's overall success in the competition.
The Attitude Benefits of Using a Math-Based Strategy
The second survey measured students’ attitudes toward math and robotics in general. Figure 2 below shows the results from each Focus Team for this survey. Only 1 of the 4 Focus Teams had more positive views in each part of the attitude survey after the competition compared to before, and that was Team E2. Team E2 was the elementary school age team that used the math-based Calculate-Test-Adjust strategy in their solution. For this team, the experience preparing and competing in the competition did have a positive impact on their interests in robotics and mathematics, as well as their views about the value of mathematics in robotics.
Remarkably, this positive change in attitudes was attained in spite of the fact that Team E2 did not score highly in the actual competition (ranked #17 out of 22 teams). This result echoes a statement by a number of other coaches who, in the day-of-competition team interviews, stressed that they were participating to provide their students with a positive experience in robotics, not to win the competition. Perhaps it worked. It appears, though, that by using mathematics in the robotics competition, attitudes toward math itself get caught in the updraft, and benefit as well.
There are number of positive outcomes that result from participating in a robotics competition. Better problem solving and more positive attitudes toward robotics and mathematics are two outcomes that appear to be attainable. These are in addition to, and possibly even preferable to, performing well in the competition itself!
Conclusion #3 – Even when a team's use of math doesn't lead to success on the challenge, just attempting to use math can have other benefits in terms of improving students' understanding and developing more positive attitudes about math and robots.
This series has been about finding out what makes successful teams successful. Being older, more experienced, and better at math sure seem like advantages for teams in a robot competition. But those are hardly the point, or even the whole story.
The use of mathematics in solution strategies, however, is very much to the point. Every coach has this option, and it appears to pay off in both tangible and intangible ways. A team with a high degree of fluency in mathematics can apply math in creative ways to springboard themselves to the top of the charts.
A team that is less comfortable with mathematics but commits to using math anyway sets itself up for a different kind of success – real, measurable gains in student problem-solving capability and attitudes toward robotics and math. If, in trying to create more systematic solutions, students' failed attempts actually help them to understand more about the way the robots work, they will be able to apply those improved understandings to future problems. If, in the challenge of attempting to use math, a student comes to understand the role or context of mathematics better, it makes both robotics and mathematics more interesting, and helps the student to see math as having real, usable value in robotics and the world.
And that certainly sounds like a success any FLL coach would be proud to report, trophy or no.
Thank you for reading our series on the benefits of math in LEGO robotics competitions. We hope that you found some useful information to think about when working with your team this year for the upcoming FLL competition. Please leave comments to let us know your thoughts on our articles and on the use of math in educational robotics more generally. Also, consider volunteering to help us in our next investigation. There are still many open questions about what helps a team be successful, and we hope to continue to investigate those questions and share what we find with the FLL community (send an email to Eli Silk if you are interested).
In actuality, five teams agreed to be Focus Teams, but one team’s data was incomplete and therefore not fully counted. The patterns observed do continue to be true even if the incomplete data is left in.
The number of students on the Focus Teams reported in the table is the actual number of students who participated in team activities. This is sometimes different than the number of students who completed the surveys. The surveys were only given on a particular days, on which some students may have been unavailable. The number of students who completed the surveys for each Focus Team is shown in the x-axis of the results figures for the surveys.
Written by Eli Silk
August 25th, 2010 at 11:25 pm