I just love the feeling I get when the skills that I have taught my students transfer over to a different content area or a new environment. It solidifies that I have taught them more than just a concept, but a life-long skill that they are indeed putting into practice. The skill I have noticed lately is perseverance.
I really love how ZONES cultivates perseverance with students. Perseverance in mathematics has become quite a hot topic/buzz word lately. I have also seen it being discussed as a "growth mindset". When students persevere through a posed mathematical problem they must see themselves as capable of and effective at learning and doing the mathematical concepts both with skill set and effort.
Perseverance is also viewed as an essential piece of mathematic proficiency. In a National Research Council report, Adding It Up: How Children Learn Mathematics (Kilpatrick, Swafford, & Findell,2001), highlights “productive disposition” [perseverance] as one of five key “strands” of what it takes to be mathematically proficient. They explain that “productive disposition” [perseverance] is interdependent with four other “strands of mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning.”
Perseverance is a very interesting skill. Research suggests that students’ out-of-school experiences influence their perseverance with mathematical tasks. Tasks that have a familiar or real-life context are more meaningful. Because students are able to draw on their everyday experience to solve these kinds of tasks, they are more motivated to stick with the task (Taylor, 2015).
However, what if the students have little academic background knowledge to draw from? The students in my school are highly at risk due to multiple factors such as poverty, family instability and dysfunction, school environment and community resources, English as a second language, and minority youth. They have very little academic background knowledge to pull from when tackling a math problem.
Perseverance is also influenced by the norms of the classroom, particularly a student’s perception about her mathematical ability relative to other members of the class. “Students compare themselves against the norms of mathematical competence in their class[es], construct sets of ‘stories’ that define their own proclivities and handicaps, and use these stories to help them decide when and to what extent they will engage in the social activity of doing mathematics” (Middleton, Tallman, Hatfield, & Davis , 2015). They often think that perseverance is something that some students are skilled at rather than a behavior that everyone can develop. However, as students get older, they begin to have a self perception of their math ability. In my math class in particular, we group our students. My group consists of students at a below grade ability level. By fifth grade, these students have already experienced failure, lack of support, and the awareness that peers are "better" at math.
Perseverance is at the root of the ZONES framework as it is the first Common Core Mathematical Practice Standard (which are the building blocks of ZONES). And even more inspiring, perseverance CAN BE TAUGHT!
I will go into detail in my next post how we go about explicitly teaching it. AND IT WORKS! Recently my students had to take the dreaded State Standardized test. During this test I saw how my ZONES students persevered beyond their peers. I saw them try strategy after strategy to try to determine the answer. This was with mastered skills as well as with new foreign skills. I was so proud of my students during this difficult testing time. I know that state government puts a lot of emphasis and pressure on students' final scores on this test. However, I was just so proud of their effort and perseverance. The fact that they tried and kept trying is a skill I have seen develop over the last 8 months of school. It is also a life skill that they will use in varying situations throughout their lives, both academic and realistic.
Keep trying out there! We teachers need to persevere during these last few months of the school year too!
Hyman Bass and Deborah Loewenberg Ball. (April 2015) Beyond "You Can Do It!" Developing Mathematical Perseverance in Elementary School. University of Michigan http://www.spencer.org/sites/default/files/pdfs/bass_ball_mip_0415.pdf (April 27, 2017)
http://www.corestandards.org/Math/Practice/ (April 27, 2017)
https://en.wikipedia.org/wiki/At-risk_students (April 27, 2017)
http://www.ascd.org/publications/books/104017/chapters/The-Importance-of-Background-Knowledge.aspx (April 27, 2017)
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: How children learn mathematics. National Research Council, National Academies Press.
Middleton, J. A., Tallman, M. A., Hatfield, N., & Davis, O. (2015, April). Taking the severe out of perseverance: Strategies for building mathematical determination (White paper). Chicago, IL: Spencer Foundation. Retrieved from http://hub.mspnet.org/index.cfm/28128
Pasquale, Marian. (2015) Productive Struggle in Mathematics. Research Brief. Interactive Studies in STEM Teaching and Learning. Education Development Center, Inc. http://interactivestem.org/wp-content/uploads/2015/08/EDC-RPC-Brief-Productive-Struggle.pdf (April 27, 2017)
Taylor, E. V. (2015, April). Cultural considerations in support of mathematical perseverance: The role of context activation (White paper). Chicago, IL: Spencer Foundation. Retrieved from http://hub.mspnet.org/index.cfm/28130
We all know the term "growth mindset" has been pretty trendy lately. But, what does it REALLY mean to cultivate it in your classroom? When the article "How to Integrate Growth Mindset Messages Into Every Part of Math Class" kept showing up in our Twitter feed, I knew I had to check it out. This is one of the opening sentences of the article:
Can you identify with the 60% who don't feel strongly about cultivating a growth mindset in your students? I know I feel that way at times.
Fortunately, this article had some concrete suggestions of what we can do... and there's something we ALREADY do!
One of the suggestions is to use error analysis, which we do quite often in the Notebook zone. I originally got the idea from Teaching With a A Mountain View (check it out for some great pre-made error analysis pages!). I modified her form for our ELLs, so that it includes a word bank and sentence starters. We do a number talk style model of what a strong response looks like before students work on the page on their own. Here are some examples from my 4th grade class from their work on the standard algorithm for subtraction.
So how does this error analysis cultivate a growth mindset? Here's what Cathrine Good, growth mindset researcher and social psychology professor says about error analysis: "Embedded in that worked example is a lovely opportunity to talk about growth mindset and mistakes and process."
Do you use error analysis with your students? How can you use this to cultivate a growth mindset in your class?
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