This week in class, we discussed various positive norms to encourage in a math class. I just wanted to briefly discuss my perceived importance of the norms developed by Jo Boaler in this weeks post:
1) Everyone can learn math to the highest levels
2) Mistakes are valuable
3) Questions are really important
4) Math is about creativity and making sense
5) Math is about connections and communicating
6) Depth is much more important than speed
7) Math class is about learning not performing
Individually, each of these norms aim to develop a positive relationship with mathematics, however, as a whole, they aim to develop a sense of community in the mathematics classroom. I believe that this is critical for students to reach their full potential. Consider a classroom where students feel comfortable asking questions, making mistakes, thinking outside the box, offering help or opinion, or taking their time to understand a concept before moving on... Now consider a classroom where students do not feel comfortable to do any one or more of these positive norms. How can we as educators expect our students to succeed without effectively introducing and consistently encouraging these norms? Setting and promoting an inclusive mathematics community should be a top priority for all math educators.
Diagnostic Assessment
It is very important for educators to understand what prior skills/knowledge their students bring with them to the table. This week, we took a look at some sample questions math teachers can use to assess not only prior knowledge, but also preferred methods of reasoning. The diagnostic question we analyzed was called "Making Juice". Essentially students were asked to decide/rationalize which of 4 cups of juice was the most concentrated. The 4 cups were as follows:
1) 2 cups of orange, 3 cups of water
2) 1 cups of orange, 4 cups of water
3) 4 cups of orange, 8 cups of water
4) 3 cups of orange, 5 cups of water
First, we were asked to solve the question on our own. I used fractions and percentages to solve that the first cup was the most concentrated with a value of ~66.67%. Next we were asked to examine some student solutions. The student work I examined used circle graphs in order to visualize the answer. His/her visual depiction was as follows:
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| Sample Student's Work - Image created on MS paint |
For me, the activity really opened my eyes to several things:
-the amount of thought that is required to develop good test questions
-how much more important the rationale is than the final answer (think journey vs destination)
-how much one question can tell you about a students prior knowledge and method of reasoning
Each of these "takeaways" are so important to remember when assessing students not only diagnostically, but also in formative and summative situations. Consider the student work above...the student was able to get the correct answer without understanding how to properly solve the question. If this question were multiple choice on a test, the student would have gotten 100% for a question they essentially modeled incorrectly. Although their journey led them to the destination, they are just as far away from when they began. Who knew that something as simple as asking a student to provide rationale for their answers could yield such powerful information?
Relating diagnostic assessment back to positive norms, it is important to keep in mind that your students are very good at "picking up" on what you value as a teacher. For instance, if your diagnostic assessment on the first day of class is a formal test, you are setting the tone for the community that doesn't necessarily reflect well on the positive norms...remember, consistently encouraging the positive norms is just as, if not more important than introducing them.
Great post Kevin,
ReplyDeleteI really enjoyed reading your understanding of Boalers positive norms in the classroom. I strongly believe the most successful classrooms have developed a strong sense of community within them. It's the teachers responsibility to cultivate that positive, inclusive learning environment.
This movement towards the a successful classroom community has always seemed a little challenging in my mind. However, I am sure that focusing on incorporating Boalers positive norms into the classroom would be a solid foundation to the classroom community I hope to develop in my classrooms.
Cheers,
Mike S
Hi Kevin!
ReplyDeleteI like how you discussed building a sense of community within the classroom. As a former high school student I often felt next to no sense of community within my math classes, some students understood, others were confused, and even more students simply didn't care. I think we need to find more ways to engage students as a whole in the classroom, and build that sense of community that the students so deeply need.
Again great read!
Brodey Holditch
Kevin,
ReplyDeleteI like how you discussed in detail the diagnostic question that was analyzed in class. I found it interesting to see the different approaches students had used to find an answer. Like you said, a lot of important information comes from the rationale provided as a student could reach the right answer from the wrong conceptual understanding. This proves the importance of a meaningful diagnostic assessment.
I also like how you mention that students pick up on what you value as a teacher. In my future mathematics classroom, I will definitely be encouraging Jo Boaler's positive norms every day.
Great post,
Julia