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Writing to gain ownership It has been my experience that students often believe that they “understand” a concept while it is being demonstrated by the teacher. Even as they listen to classmates answer questions, they may have a sense of confidence of their own ability to similarly perform the task. However, it is not until they put pencil to paper (or marker to whiteboard) that they have evidence of that comprehension. “The only way we know students have learned something is if they demonstrate recall of it." (Jenson 99) If we as teachers wait for the chapter assessment, it is much more difficult to correct the errors and the student may lack the foundation on which to build subsequent content knowledge. As important as the teacher’s ability to assess a student’s learning is the increased depth of understanding available to the student through the process. “The more students talk about mathematics, the more students learn about mathematics.” (Sherin, Mendex, Louis 232) Often it is through writing and talking with their peers and their teacher that the students refine their understanding and fill in the gaps of the learning.
Eric Jenson in his book Teaching with the Brain in Mind explains the rational for reflective summary exercises like learning logs. He states: “In the classroom, there is value in focused learning followed by diffused activities like reflection. There are three reasons why... First, much of what we learn cannot be processed consciously; it happens too fast. We need time to process it. Second, in order to create new meaning, we need internal time. Meaning is always generated from within, not externally. Third, after each new learning experience, we need time for the learning to imprint.” (46) “The essential point here is that teachers must encourage ‘personal processing time’ after new learning for material to solidify.” (47)
Brain research verifies that learners make sense of new information through connections to what they have previously learned. The brain is able to store information in long-term memory through these connections. As students are able to summarize and organize their knowledge through the writing process, their understanding and retention of that topic increases. As teachers read their students’ writings, they are able to gain greater insight into their students’ understanding, which provides another benefit from student writing.
Jeremy Kilpatrick and Edward Silver conclude the NCTM 2000 yearbook with a chapter focused on challenges for math educators. They remind us that for our students to truly learn they must interact with the knowledge themselves as more than just recipients of our insights. “Learning has never been simply a matter of acquiring and retaining information; for information to become useful knowledge; it must be transformed by making it one’s own, looking at it from all sides, seeing its interrelations, and thinking about its meaning. In other words, the learner must somehow reflect on his or her learning if it is to be put to use. “(232)
I chose the strategies of learning logs and white board work because in each the students must reflect upon and then put in writing their knowledge and application of the content. Because the strategies elicit work that is both personal and individual, the students are provided the opportunity to process and internalize the content we are working on. Through the guided questions in the learning logs, they are asked to make connections to prior work and see where this concept fits in the bigger picture of mathematics.
My teaching has been greatly influenced by the work
of David R. Johnson, Every Minute Counts: Making Your Math Class
Work. I shared his frustration that two or three students wanted to
answer all the questions posed and the remaining students wanted to be left
“un-called-upon.” While this traditional approach may provide me
information on those two, they are far from representative of the level of
class comprehension. Johnson explains, “The teaching of a new concept should be much more than a how-to-do-it demonstration, a lecture, or a show—although all of these procedures may be part of the teaching. Student involvement is essential, and that involvement should be meaningful and include all students. While I’m teaching, I need to be aware of each student’s level of understanding. At the same time, students themselves need to know how well they understand the concept I’m teaching and whether they are able to use it themselves to solve problems. If I lecture or demonstrate neither I nor the students are getting this kind of information. … [Students] need to be involved in the actual teaching of the objective. Such student involvement demands frequent use of paper and pencil…” (31) During class, using the individual whiteboards allows me to see the work of each student and to provide immediate affirmation or correction. I know to continue the guided practice until most, if not all, of the students can demonstrate proficiency. Students cannot hide, but must interact with the content. |