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# April 2013

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• 1. The Learning Space Seems we hear so much about student-centred classrooms involving collaborating learning, teachers moving about the room for small group instruction, teaching through manipulatives, interactive white boards and math applets or digital learning supports, does anyone ever talk about the chalk board (or whiteboard) anymore? Even though we are changing our practice to involve students more and provide more experiential learning, there will always be a necessity of some explicit instruction in mathematics. Our subject is extremely visual and procedural. Marzanno (2004) lists explicit instruction among instructional strategies that have significant effect size. Intensive-explicit instruction can be a way to efficiently teach content (Knight, 2013). It is the reality of math instruction that we need to demonstrate by writing, using symbols and diagrams, either on a chalkboard, whiteboard, or interactive board. Even though we want to spend lots of time circulating around our classroom and interacting with our students, we still need a focal point in the classroom. Modeling logic and thinking are extremely important instructional practices. As we write our mathematical processing on the board, we are modelling logic and representation. Our own organization or lack thereof will be reproduced in student notebooks. If we want our students to have a collection of class notes that are useful for reference and review, then we need to attend to the logic and order with which we present the material. Some things to consider are: 1. Visual Learners: It is estimated that between 30% and 65% of our students are visual learners. These students rely heavily on the representations that we write on the board. Sometimes after we have finished talking and explaining and have moved on, these students are still looking at what we’ve written and represented. All students must learn visually in math some of the time. Visual learners also benefit from multimedia, use of colour, and manipulatives. 2. Cognitive Overload: Students that struggle with math are processing slowly. Often we design exams with lots of white space for these students, because they need to concentrate on a small amount of material at a time. The same is true with how Effective mathematical Communication involves expression and organization of ideas and mathematical thinking (e.g., clarity of expression, logical organization), using oral, visual, and written forms (e.g., pictorial, graphic, dynamic, numeric, algebraic forms; use of conventions, vocabulary and terminology of the discipline (e.g., terms, symbols) in oral, visual, and written forms . Ontatrio Ministry of Education, 2005 “The blackboard may be verily called the second tongue of the Mathematics teacher….It should not be used in the manner that the teacher goes on writing and drawing and the students go on copying. The entire matter to be written on the blackboard should be developed with the active cooperation of the students…Students should also be given the opportunity to write and draw on the blackboard.” K. Singh Sidhu
• 2. and what we write on the board. Many students are overwhelmed by math work on the board that is crowded, overlapping, or out of sequence. 3. Summarizing and notetaking is another instructional strategy with a significant effect size. In younger grades students may just copy what we write, but as they move into senior grades, students synthesize the information for themselves. The logic and order that we model will become part of the representation style of our students. 4. Communication: Effective mathematics instruction involves communication that is both verbal and written. We communicate, model, and explain our reasoning to students by how and what we record on the board. We need to model effective written mathematical communication that includes logical reasoning, worked examples, units, appropriate mathematical terminology, and explanations. 5. Adaptation: Since we want to adapt our teaching for students with learning disabilities, hearing impairment, attention and behaviour issues, and English as an Additional Language learners, it makes sense to include a strong visual component to our instruction. 6. Unlike technology, powerpoint, print, and video instruction, explicit instruction that includes chalkboard, whiteboard, or interactive board is very flexible. It allows the teacher to gauge understanding and adjust instruction. Though we are using direct instruction in these instances, we are still eliciting student input, assessing for understanding, and adapting our instruction to fit the learning that is taking place. The TIMSS study which compared math instruction in several countries including Japan, United States, and Germany, noted that 100% of Japanese teachers use the chalk board for part of their instruction. They use it as a record and running documentary of the entire lesson. Teachers plan ahead of time what the board will look like, what will be recorded, they record sequentially and avoid erasing. They expect that not all students will be focused in every part of the lesson at the exact time. They expect students to look back to previous parts of the lessons. Japanese students rank very high globally in math ability. It is worth noting that Japanese students are assigned less homework than most other countries, and that “Most aspects of Mathematics can be clarified only through writing. Verbal explanation will not suffice in such cases.” K. Singh Sidhu “Here, Germany and the U.S. are virtually identical—the purpose of seatwork is to practice the procedure being taught. In Japan, by contrast, teachers placed much more emphasis on getting students to come up with new ways to solve a problem that they’ve never seen before or to use mathematical reasoning to prove something. Fifty-four percent of the Japanese lessons included proofs. None of the American lessons included proofs.” From the TIMSS study. California State University Institute for Education Reform. “We found that 47% of the American lessons only included applications, without any reference to any kind of a math concept in the lesson; that is, teachers taught students that A to the M power divided by A to the N power equals A to the M minus N purely by repeating examples, rather than stating the underlying math concept. This was very rare in Japan and Germany.” From the TIMSS study. California State University Institute for Education Reform.
• 3. math is taught through problem solving (The California State University Institute for Education Reform, 1997). Some helpful hints gleaned from countless web resources and blog postings on this topic: Start with a clean board and organized learning space Create a routine: Date, title, text book page, learning target, etc. Keep writing large enough and neat. Include diagrams. Use colour. Work in sequence. Show logical steps. Model logic and order. Include margin notes, cautions, explanations, reminders, study hints, additional references. Avoid erasing too soon. Ask for class participation. Have students contribute to board work when applicable. Provide worked examples. Avoid clutter. Consider using the board as “anchor notes” while students work through collaborative activities. Use part of the board for instructions for activities. Some students have difficulty remembering and following instructions. It’s handy to be able to redirect them to the activity instructions, group member, group roles, expectations, etc. that are recorded on the board. Look at how and what students are recording in their notebooks. Provide specific feedback. Instructional Scaffolding Means providing supports for students to enhance learning and aid in the mastery of tasks. Content Task Material Instruction -Riccomini, P. 2012 High Impact K-8 Mathematics Teaching Strategies to Maximize Learning Of Essential Skills and Concepts References: Brown, A. The Advantages of Using Chalkboards in Teaching. http://www.ehow.com/list_5872788_advantages-using-chalkboards-teaching.html Retrieved April 2013 Buddle, C. In praise of chalk: the value of teaching without technology. http://arthropodecology.com/2012/04/11/in-praise-of-chalk/ Retrieved April 2013 Jones, K. Teaching Math to a Visual Learner. http://www.time4learning.com/teaching_math_to_visual_learner.shtml, retrieved April 2013 Knight, J. (2013). High-Impact Instruction. Thousand Oakes, CA.: Corwin Press. Lessons in Perspective: How Culture Shapes Math Instruction in Japan, Germany and the United States. A discussion sponsored by The California Education Policy Seminar and The California State University Institute for Education Reform. http://www.csus.edu/ier/reports/math.pdf Retrieved April 2013 Riccomini, P. High Impact K-8 Mathematics; Teaching Strategiesto Maximize Learning. Webinar, Nov. 2012 Singh Sidhu, K. (2006). The Teaching of Mathematics. Okhla, New Delhi. Sterling. Teaching Math To A Visual Learner. http://www.time4learning.com/teaching_math_to_visual_learner.shtml Retrieved April 2013 Teacher tips: Understanding the visual learner. http://www.helium.com/items/1762331-educat-teach-communicat-visual-learn-style-thought-brain- cognitive-skill-ability-school Retrieved April 2013