Once she began to present this argument, I basically smacked myself in the forehead (literally) and said, "of course!" Of course a student needs to know and understand that a mistake is an opportunity to grow. I realized that a part of me has always assumed students do this. But they don't. Boaler has convinced me that many students still have the fixed mindset.
Fortunately, Boaler's main goals is to help us think and teach about the growth mindset. She discussed the reactions of a child to their school day:
"Math is too much answer time and not enough learning time."
When we rush kids, we encourage the fixed mindset. But it is essential to give them time on the content and intuition of any math problem you present. Here are the basic growth mindset elements she shared:
These elements are major components to every successful lesson I have ever given. Boaler starts with "openness", which leads to opportunities for "different ways to seeing" an answer. This by definition encourages students to find "multiple entry points" to the problem. With different paths to choose in their strategies, students will have opportunities for rich conversation in the lesson and opportunities to give "feedback." Its a collaborative and intuitive model. It is also simple in structure and thus portable and useable for other teachers.
Boaler gives a significant amount of research and references to show the importance of feedback. This ties into the philosophy of different mindsets and has some surprising results. These studies have already really made me think about the role of assessment and feedback in my classroom.
In one study, students were given three different types of assessment:
In the first group, students received grades from the traditional summative assessment model. This was my high school experience. You work and get a grade for your efforts.
The second group was simply given diagnostic feedback. Diagnostic feedback is like the standards based grading model without any grades. Instead, they offer simple one sentence feedback, like "you worked really hard to get that concept. I wonder if you would like to go a bit further?"
The third group was given both the traditional and standards based grading model (something that I work with, posts coming eventually).
The surprising result is that the students who received no grades at all (the diagnostic model) outperformed the others.
The idea is that the diagnostic model helps students identify what they need to know. As Boaler states, "But they found that the very best thing you can do for students is to ditch the grade and give them diagnostic feedback. And that feedback helps them understand how they can improve."
Many students struggle because they are not sure of what they already know and where they are going next. Helping students recognize their progress and see the next steps is paramount.
Diagnostic feedback can look a lot like standards based grading and my sense is that the line between the two is certainly blurred. Boaler gives an example of a learning goal or standard:
I like the idea of working the standard into a statement that students can actually say. It gives merit to their work when they read the standard, something more than just "measures of central tendency" and an actually statement that they can recite out loud or to themselves, "yes, I do understand the different between mean and median and know when they should be used."
Another study built upon the diagnostic feedback idea and split students into a group with class discussion (traditional chalk and talk teaching) and a group that utilized peer and self assessment (variations of themes in standards based grading).
The amazing result here is that all students at all levels improved in the group that focused on peer and self assessment, especially the lowest achievers. They responded so well that they started to exhibit the learning behaviors of the highest achievers. This goes back to the simple idea that you can only be successful if you are aware of what you currently understand and what you need to understand next.
The last major study that Boaler mentioned compared the work of students who are tracked, or separated by their grades and students who are mixed together, regardless of their achievement levels. I am a strong opponent of tracking and am excited to see studies that back up my thinking around this matter.
Here were the major points of the study:
The logic for these results is quite simple. Students who are placed or tracked into a section are essentially forced into the fixed mindset, thinking that they are either "good" or "bad" at math. The teachers also perceive the students in this way and give them work and lessons accordingly. This combination essentially prohibits students from understanding the growth mindset, a necessary ingredient for success in math. In stark contrast, the teacher in the mixed class must challenge all students and help all students succeed. In doing so, the lessons and work in a mixed classroom can help all students reach their full potential.
I look forward to the remaining sessions!
Here are the three studies I referenced, in order:
Diagnostic Feedback:
Butler, R. (1988). Enhancing and Undermining Intrinsic Motivation: The Effects of Task-Involving and Ego-Involving Evaluation on Interest and Performance. British Journal of Educational Psychology, 58, 1-14.
Discussion Group vs. Peer and Self Assessment:
White, B., & Frederiksen, J. (1998). Inquiry, modeling and metacognition: making science accessible to all students. Cognition and Instruction, 16(1), 3-118.
On Tracking:
Here is the study reference:
Burris, C.C., J.P. Heubert and H.M. Levin (2006), "Accelerating Mathematics Achievement Using Heterogeneous Grouping", American Educational Research Journal, Vol. 43, No. 1, pp. 105-136.
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