Reflection+Logs

**Reflection Logs**
Reflect on the activities we did in class in relation to the article.
 * ** Workshop on Feb 7 ** ||
 * I really enjoyed todays lessons about measurement of area and perimeter. It is something I will be able to use within my own classroom. I really liked how the words area and perimeter were not mentioned in the directions for finding which figure was larger. This allows students to go back to basic reasoning instead of simply plugging in to solve with a formula. Our students have lost they ability to make sense of math things because we as teachers have pushed away from that and have relied on algorithms and formulas. As simple as it was to solve which figure was larger for some groups, other groups tried to use a formula to calculate the area of the figures and subtract what it was missing. ||
 * Today's lessons were a powerful reminder how we as math teachers need to give students to time to visual and make sense of what they are doing instead of telling them "here's the mathematics chart with the formulas". ||
 * The topic of measurement is one in which we teach our learners how to measure and conceptually understand measurement first by ensuring that our learners understand the measuring process fully, looking carefully at the concepts involved in measuring different physical characteristics of physical objects, and to teach for understanding. It is important to remember this in our teaching of measurement and facilitate it by giving a good conceptual grounding followed by sufficient practical exercises, hence, the need for careful use of language if we are to avoid speaking unclearly or ambiguously. We must say exactly what we mean, and give clear instructions to our learners. ||
 * reflection log#1 ||
 * Read the article by Roger Day and Graham Jones on //Building Bridges to Algebraic Thinking//.
 * Read the article by Roger Day and Graham Jones on //Building Bridges to Algebraic Thinking//.

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 * 1) 1. What do you think is the key difference between arithmetic thinking and algebraic thinking?
 * As in the 1st Hamburger Problem, it merely asks to calculate using the information given to you. The information is presented in a form that is already set-up for multiplication, therefore there is no further thinking and you arrive at the answer without any further exploration or thinking. On the other hand the 2nd Hamburger Problem does not give you the amount of players, therefore initiating a mental transition from arithmetic to algebraic. Since the answer is not automatic in Hamburger #2 it now elicits secondary mental processes in order to distinguish between constants and/or variables. The questions then fosters a continuous thought process that helps make connections with other algebraic situations.

> [Type your response here. You may present your ideas as bulleted items.]
 * 1) 2. What important ideas (pedagogical content knowledge) that you have learned from your reading of the article and your reflecting on the classroom activities.
 * Start with an introductory question that helps bridge or guide the lesson in the direction that facilitates the next level of instruction.
 * Keep teacher probing questions or scenarios in mind, in order that you can raise the level of rigor(algebraic thinking) for any student in your classroom.
 * When posing questions, use “find a way” to solve in order to engage all students regardless of their previous knowledge.
 * By; Anticipating, Monitoring, Selecting, Sequencing, and Connecting lessons and engaging students will become the norm in the classroom.

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 * 1) 3. Create a story problem of your own that require students to “find a way to determine …”.
 * Develop an algorithm to determine the sum of consecutive even numbers.
 * Example:
 * 2+4=6
 * 2+4+6=12
 * 2+4+6+8=20
 * 2+4+6+8+10=30
 * 2+4+6+8+10+12=42
 * 2+4+6+8+10+12+…100+….240…+...nth term =Sum of consecutive even numbers ||