In September and October of last year (2014) I ran a 7 session program that I called ‘The Mathematics Applied Preparation Program' (MAP for short). For the students, it was a last sprint before their end of year exams. We covered a different one of the five topics with an additional session for introductions and one for wrap up. For me it was the bringing together of a lot of things that I'd been reading and learning over the preceding year on education, and a chance to try to put some of those ideas into action. This post is a much delayed reflection on the planning, implementation, and outcomes from the program, concluding with lessons to take forward into my future teaching. (See the program content here).
I began the program with the end in mind, and the intended learning outcomes for the students were threefold. Firstly, I wanted to introduce them to the work of Carol Dweck, I wanted to help them to understand the concept of ‘mindset' and it was my intention that participating in MAP would aid them in gaining a growth mindset (for those unfamiliar with this concept you can see a presentation I did on mindset here). Secondly, I was hoping to help students to develop higher levels of motivation to facilitate them actually doing the work required to learn the content. Finally, I wanted to help them to feel at ease with Math. This relates to not being anxious about it, and not trying to avoid it in future.
To track how the students progressed on the above metrics I designed a questionnaire (Likert scale, 6=strongly agree, 1=strongly disagree) to monitor their progress. This questionnaire was taken by students during the introductory session and then again at completion of the course. The better part of this blog post is dedicated to exploring the results of that questionnaire… were mindsets changed?
Unfortunately, the program didn't have as many students as I would have liked. Despite promotion at three schools* only 2 students attended the program from start to finish, and 3 other students only attended selected sessions on the topics of interested to them. It would be nice to have a larger sample size from which to draw conclusions about the success or otherwise of the program with respect to the three goals outlined above. But I think the process is still a helpful one, even if just to explore how I could better design and implement such a survey in future.
*Two of which I visited in person, doing a short mnemonic exercise as a taster. For the other school a flier was distributed to all students taking the relevant maths class.
How did Mindset change throughout the program?
Though I wanted to explicitly address this topic, I found it hard to track down resources to help explore the concept with students (I have since found this excellent lesson plan). The resources from Carol Dweck's work appeared pitched at younger students (the students in this program were 17 to 18). I was hoping to also find some resources that referred to brain plasticity as a basis for suggesting that ‘everyone can do maths'. I couldn't find any such resources**, so decided to take a bit of a different approach. The approach would be that simply through giving them an experience of success in mathematics, they would hopefully have first hand experience that they could do it. I based the mindset component of my questionnaire on the test found on Carol Dweck's website. Here are the results (S1 (Student 1) and S2 attended the entirety of the program. S3 only attended 3 sessions).
Summary: Looking at the mindset scores in the rightmost column, both students who attended the entirety of the program saw increases in their mindset scores (10 points and 7 points respectively), indicating increases in growth mindsets. Student 3 saw a drop in mindset score, but only of 3 points. Obviously the reliability of these scores is debatable, however hopefully they are generally reflective of increases in growth mindset.
An improvement I would make in future would be to use simpler wording in the second and eighth questions to ensure that students aren't misinterpreting them. I will apply this improved version of the mindset quiz in future to monitor mindset changes in my classes.
**It is the claim of Malcolm Gladwell in his book ‘Outliers' (primarily based on the work of Anders Ericsson) that anyone can attain a level of elite performance with sufficient deliberate practice, with reference to ‘the 10,000 hour rule', i.e., 10,000 hours is roughly the amount of time it requires to attain elite status. Ericsson claims that “It is possible to account for the development of elite performance among healthy children without recourse to unique talent (genetic endowment)—excepting the innate determinants of body size” (Ericsson, 2007, p.4) “. This was a revelation to me when I first heard of it, and I immediately started quoting it to students. Unfortunately, I have since found that the initial research proposing this 10,000 hour rule had some serious flaws (See the work of David Humbrick and colleagues). Interestingly, John Hattie identifies five major dimensions of excellent ‘expert' teachers, one of which is the following.
‘Expert teachers believe that all students can reach the success criteria: Such an expectation requires teachers to believe that intelligence is changeable rather than fixed (even if there is evidence to show it may not be…).' (Hattie, 2013, location. 697).
An interesting dilemma for teachers, and one I know I'll continue to grapple with…
How did motivation change throughout the program?
I knew that the students coming into the program had low motivation levels, so I tacked on a few questions to the survey in an attempt to diagnose their motivational weak points. The motivation centric questions in the survey were based on the procrastination equation (which I go into more detail about here). Essentially, Steel (2007) writes that procrastination is a function of three qualities or attitudes with 4 sub-beliefs/factors. Here is a screenshot from my learning model mind map that details these factors.
Here is the survey results for the motivation section of of the survey. The light blue row indicates which of the factors each of the questions relates to (2 for each factor. Note: The order in which the questions appear here is not the order in which they appeared in the survey, there were split up in the survey).
Click for larger view
(Motivation score algorithm: =N7+(7-O7)+P7+(7-Q7)+R7+(7-S7)+T7+(7-U7)+V7+(7-W7))
We can discuss each of the students one by one (or you can jump 3 paragraphs ahead to the summary).
Student 1 showed a small increase in time sensitivity, no increase in the belief of relevance of mathematics to his life, an increase in how boring he found mathematics, an increased belief that he could achieve in mathematics, but a decrease in his belief that he knows how to study. In summary, Student 1 demonstrated decreases or no change in all but 1 of the motivation metrics.
Student 2 displayed no change in time sensitivity, no change in their views on the relevance of mathematics to their life, a 2 point increase in both of the questions relating to their enjoyment of mathematics, a slight increase in their belief that they can achieve in maths, and an increase across both questions relating to a feeling that he knew how to study well and improve his skills in mathematics. Student 2 showed no change or an improvement in all metrics related to motivation.
Student 3 showed an increase in time sensitivity, a decreased belief in the relevance of mathematics to their life, a decrease in their enjoyment of mathematics, a decrease in their belief that they can achieve in maths, and a slight increase in their belief that they know how to study effectively. Thus, an improvement in two of the motivational metrics and a decrease in 3.
Summary: Looking at the aggregated motivation scores, student 1 demonstrated a 3 point decrease in motivation, no change for student 3, and a 10 point increase for student 2. As with the mindset results, the reliability here is definitely uncertain.
How did anxiety and avoidance attitudes change throughout the program?
Anxiety is on factor that I knew could potentially be significantly compromising student's test performance. This is as anxious thoughts take up space in working memory and reduce processing power allocated to the actual mathematics (more on that here). As such, I wanted to ask students if their anxiety about mathematics reduced over the course of the program. I also knew that actions speak louder than words and one big indicator of whether students' attitudes towards mathematics had changed was whether they would avoid mathematics in future. Top right are the 2 questions and the results relating to these two points (again: 6 is strongly agree, 1 is strongly disagree).
Two students were more anxious and one did not display change in their self rating of anxiety. Two students wanted to avoid maths more in future and, again, one did not change his self rating. There was , however, overlap, so all students saw decreases on at least one of these metrics with none displaying an increase.
Final reflections
The program was fun to run. It was my first move from the role of a reactive tutor to the arena of ‘curriculum design'. I relished the chance to plan out 7 sessions of 2.5 hours each in which to try to address the big issues of mindset, motivation, and anxiety in tandem with helping them to gain greater success in their final exams and general understandings of the mathematical concepts. Success? Well, I learned a lot and I feel I formed some strong bonds with the students. The major lesson for me, aside from this being my first attempt at actually measuring the impact of my teaching, was about keeping a tab on the cognitive load that you're putting on students and not trying to cover too much in a session. There's a fine line between guiding students to deeper knowledge and drowning them in a barrage of information. It's a balance I've continued to try to find in my current educational engagement, My Masters of Teaching semester 1 month placement in a Melbourne High School. Watch this space for the lessons I've been running, the lessons I've been learning, and the pedagogical techniques I've been trying over the past 3 weeks with my year 9 Mathematics classes!
References:
Ericsson, K. A. (2007). Deliberate practice and the modifiability of body and mind: Toward a science of the structure and acquisition of expert and elite performance. International Journal of Sport Psychology, 38, 4–34.
Hattie, Visible learning for Teachers, Kindle version
Steel, P. (2007). The nature of procrastination: A meta-analytic and theoretical review of quintessential self-regulatory failure. Psychological Bulletin, Vol 133(1), 65-94. doi: 10.1037/0033-2909.133.1.65