Thinking Classrooms and Consolidation and Feedback
Hello.
In this blog I want to discuss what we do at the end of the lesson, consolidation of students’ thinking, and how we evaluate their thinking processes and outcomes.
Peter Liljedahl, in his book Building Thinking Classrooms in Mathematics, uses the term consolidation when referring to the conversations teachers have with students at the end of a lesson to tap into metacognitive thinking skills so students are thinking more deeply about the math concept, problems, vocabulary and their ability to solve the problems. Many teachers refer to this as math talk, the point in the lesson where students share how they solved a problem, what worked and what did not work. It also allows students to compare their work with the work of other students and see that there are more than one way to solve a problem.
There are different ways to structure math talk, or consolidation. Liljedahl found that some consolidation methods were more effective than others. Consolidation that involves the teacher reviewing how a problem was solved and the students followed along was found to be the most ineffective. Liljedahl referred to this process as leveling to the top, or showing all students how to solve the problem, even the students who are struggling and do not understand the concept. Leveling up brings these students, and all students regardless of understanding and ability, to the top so the teacher can move on to the next step. Consequently, some of the students who level up do not have a solid foundational understanding and will be less successful moving forward to the next step. This is a compounding problem (pp.171-173).
Liljedahl worked with teachers to try different methods of consolidation. First, rather than start the consolidation process at the desired end point teachers want students to reach, they start at the base, or the foundational knowledge that the concept is built on. They start with the problem everyone was able to solve using discussions between the teacher and the groups. Using this strategy, teachers were able to build a bottom up consolidation discussion that helped all students develop a more concrete understanding of the math concept. This strategy also increased student engagement and participation, (p.173). Other methods of consolidation that Liljedahl found positively impacting engagement and participation were standing during discussions, physically moving around the classroom to view the work of different groups, groups presenting the work of other groups and using the students’ work to develop the big idea rather than the teacher writing it on the board (pp.172-176).
Now that students are participating and engaged, how do teachers provide feedback on their thinking processes? What is the value of evaluating it? Liljedahl notes that “what we choose to evaluate tells our students what we value,” (p.210). This is a critical concept. If teachers want students to engage in the thinking process and stretch their understanding to expand their knowledge, teachers need to communicate to students that thinking is important. They need to provide feedback to their students on their thinking ability.
Liljedahl found that a rubric co-created with students as the formative assessment tool was an effective way to provide feedback to students. He worked with teachers to survey students on what skills students needed to be successful in a thinking classroom. The consistent top three answers were perseverance, a willingness to take risks and the ability to collaborate, (p.209). Liljedahl also found that deviations from a traditional rubric made it more user friendly for students. For example, Liljedah removed the headings at the top of the rubric and replaced it with an arrow that moves left to right. This small change reinforced a growth mindset by allowing students to see themselves on a continuum rather than defining themselves by a finite point, (p.213, 217, 218).
Other changes that Liljedahl implemented included focusing on students actions rather than acquired skills, reducing the number of columns to three (third grade and up), defining the low end and high end of the rubric, leaving the middle column empty, simplifying and reducing language, using a two column chart with clear language and pictures on the presence or absence of skills for young children (second grade and lower) and using students’ language from the survey in the rubric, (pp. 214-219). Liljedahl and teachers found that students were more likely to incorporate the feedback from these rubrics because the focus was now growth orientated along a continuum, and because the language was simplified, which increased students’ access and integration with their daily learning, (pp. 219-222).
One other key concept that Liljedahl noted was that teachers cannot get to every student in every group on every day. Rather, the teachers shared the rubric with students so the students could rate themselves after each lesson, and the teachers chose specific students to score using the rubric. In this way, the teachers created a manageable feedback system with students, and students received daily, meaningful feedback from themselves and occasionally from the teacher (pp. 221, 222).
As a teacher and a tutor, these are concepts I need to integrate into my daily teaching. I am a proponent of math talk, but I have used a very structured system in the past. Going forward, I want to use this bottom up consolidation strategy to help my students solidify and expand their knowledge. I also want to introduce a feedback rubric to my students so they can see their growth over time.
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