After my CT's observation, she was introduced to a strategy that would help students collaborate to solve problems in Mathematics. The strategy is called a consensus map. In a consensus maps, student groups, usually of 4 or less students, work on one piece of chart paper, divided into equal sections plus one empty box in the center of the chart paper. Students are then given a real world problem to solve. For 3 minutes, students work independently in their own section to solve the problem using suggested strategies, or any strategies they are comfortable with (depending on the purpose of each particular lesson). Then the students are given 3 additional minutes to discuss their findings with their group and come to a consensus of what the most reasonable, or correct answer, is. The students then write their agreed upon answer in the blank box in the middle of the chart paper.
Since this strategy is new to me, I wanted to document some pros and cons that I noticed about the consensus maps during the lesson. For the positive, it gave opportunity to collaborate with others, which is ultimately what we want from our students. It also provided students opportunities to solve using their chosen strategy, but then compare their work to others, sometimes convincing them to use a new, more efficient strategy based on the arguments of their teammates. A consensus map is also a great way to differentiate instruction for our students. For this particular lesson, my CT was able to group students based on ability, and provide problem solving problems appropriate for their level of mathematical understanding. We were able to see how students solved in their groups, and then based on their work, some students were regrouped to either provide more support, or more enrichment. There were so many grouping possibilities, and since the students were not aware of which questions other groups were solving, they were not able to tell which ability group they were placed in. This strategy also provides great opportunity for formative assessment throughout lessons. Now for the negative, I noticed during discussions, that some students did not defend their work in order to suggest its placement in the consensus box, they would simply suggest that the "smart" kid's answer go in the box. This did not happen in all of our groups, but in some of our lower level groups, students lacked confidence in their work, and therefore were not willing to share with their group, but simply agree on whoever's work the group chose to go in the box. This is something that we want to avoid. The other thing I noticed, is that students will sometimes explain their strategies to others, and the groups will come to a consensus, but the students do not use strategies to check their work for accuracy. For example, when multiplying 1/4 divided by 4, students could use the inverse operation to check their work when discussing with their group, however most students will agree with each other quickly without asking for proof of accuracy or explanation. Usually myself and my CT rotate around the room and how the students questions like "How do you know?", and "How could you check to see if you're correct?", but the students usually will not use this type of questioning behavior with their groups or partners.
Based on what I observed from this strategy, I would like to try to use it next week in one of my lessons, with a few modifications. I want the students to be able to self check their work, so I intend on giving them an additional 1 minute during the stage when they come to a consensus. During this 1 minute, I will require the students to use 1 strategy to double check the answer they come to a consensus on. They can use any double check strategy they know, but I want them to put their original answer as well as their proof in the consensus box. I think the students need to become habitual in double checking their work, and I think this addition to the process will also produce some additional conversations within the group.
This reflective post shows evidence of my achievement towards the following FEAP(s) goals:
(a).1.c- Designs instruction for students to achieve mastery.
(a).1.d- Selects appropriate formative assessments to monitor learning.
(a).1.f- Develops learning experiences that require students to demonstrate a variety of applicable skills and competencies.
(a).2.h- Adapts the learning environment to accommodate the differing needs and diversity of students.
(a).3.b- Deepen and enrich students' understanding through content area literacy strategies, verbalization of thought, and application of the subject matter.
(a).3.c- Identify gaps in student students' subject matter knowledge
(a).3.f- Employ higher order questioning techniques
(a).3.g- Apply varied instructional strategies and resources, including appropriate technology, to teach for student understanding.
(a).3.h- Differentiate instruction based on an assessment of student learning needs and recognition of individual differences in students.
(a).3.i- Support, encourage, and provide immediate and specific feedback to students to promote achievement.
(a).4.b- Designs and aligns formative and summative assessments that match learning objectives and lead to mastery.