I liked the variety of ways to facilitate reflection: individual writing activity, drawings, notations, and collectively share ideas and then expand upon the ideas of others. I think the teacher should allow time for both individual and group reflection. Individual reflections can be shared with others, whether it’s think-pair-share or posting of drawings and notations on chart paper or whiteboards. Sharing the individual reflections with an audience makes them more authentic because the ideas are being communicated to others. Chapter 4 also mentions using individual written summaries as exit slips to assess what each student has learned from the lesson (51). I have had little success with exit slips in my practicum. Students tended to misuse them, and wrote inappropriate comments. I am more likely to use in my classroom the creative options in the text of asking students to write a newspaper headline to describe the day’s activity and a brief column to summarize it. I would probably ask them to summarize it in a 140-character tweet instead of a column. I have had success in ELA lessons with asking students to write a potential test question based on the lesson(s), so this strategy might work well in a math class, too. Chapter 18 also suggested asking students to write how they solved a problem, explain how they used the ratio table, or respond to specific writing prompts or sentence starters (364). I like these ideas, too.
I disagree that homework should be an option for a follow-up activity or assessment. For example, my son is in Grade 3. He wakes up at 6:30 a.m. His school day runs from 8:30 a.m. to 3:20 p.m. He plays minor football and practises three nights a week from 5-6:30 p.m. He gets home about 7 p.m. (7:45 p.m. if his sister is playing rugby), eats supper, showers and is in bed at 8:30 p.m. His class has a home reading program, so he sets aside time on the weekend to log reading minutes. This year, he is bringing home a math worksheet that is to be completed before Friday. He works on it while he eats breakfast. Students have obligations outside of the classroom. It is unreasonable for teachers to expect students to carve out additional time for homework after spending a day with them in the classroom. Plus, parents become resentful because they feel like they are being burdened with what should be the “teacher’s job.”
Both Chapter 4 and 18 stress connecting to students’ interests and experiences. I read an interesting blog at http://www.edutopia.org/blog/why-math-karim-ani?utm_content=blog&utm_campaign=why-math&utm_source=twitter&utm_medium=socialflow&utm_term=quote this week that says “a math class without authentic applications is like an astronomy class where students spend the year calibrating a telescope but never actually look at the stars. Math allows us to better understand the world and to live more meaningfully in it.” Proportional reasoning does not sound sexy, but is the cornerstone of a wide variety of essential topics in the middle grades and beyond (352). Proportional reasoning is important outside of the classroom, too. The Ratios as Rates type of ratio is one most people use every day when considering kilometres per hour, dollars per kilogram, and roses per bouquet (353). The questions that ask students to calculate interest and tips are easy sells because they are everyday examples. Can't think of an everyday example? As an exit or extension activity, ask students to write a problem, diagram, or pattern that relates to his or her particular area of interest. Sometimes, students may see connections between academic material and interests that the teacher does not. And everyone wins.