The testing of a task went horribly right. Background: Graham Fletcher (@gfletchy) tweeted an Open Middle (@OpenMiddle) prompt for comparing fractions. The thread debated whether or not a representation on a number line would be best. Many people liked the number line better, but I decided to stick with the inequality signs because: Students see this type of two-bounded inequality notation with domain and range. The number line gave the impression of a single, fixed answer (because the fractions appear a definite, scaled distance away from each other). I gave this question as a starter to a group of my grade …
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FractionTalks.com
I have been thinking about extending the Fraction Talk love ever since I wrote this initial post in June 2015. I have used them with my grade nine classes as the starter during units on rational numbers. I have taken the larger questions (such as “What possible fractions can be shaded using this diagram?”) as the prompt for entire lessons of student activity. I have used them to create great conversations with grade 7 and 8 students at our school’s annual math fair. I finally found the time (honestly, I found the tech guy… many thanks to @evandcole) to begin a collection …
Continue reading »Clothesline Series
I joined a middle years math community organized by my school division. I have a growing interest in the transition of students from middle school to high school because many of the tasks I use or create get at middle years content. I’m wondering what knowledge students come to my room with and what atmosphere it was learned in. Both have huge impacts on how students operate in my room.I was surprised to hear that middle years teachers lamented that students could not use number lines. I use number lines as a support in my high school classes because I …
Continue reading »Navigating Collectivity: Grade 9 Fractions
“I hate fractions” – Everyone Today an amazing thing happened; students put aside the endemic disdain for rational numbers and had a conversation. I’d go further, they weren’t discussing their views on fractions, they were collectively conjecturing–the moves of the room enacted each other. I don’t think that a written document can capture the movement of the body of learners, but I have to try something. Think of it as less of a remembering and more of a re-membering, a reconstruction of a living learning event from the past. My intern and I have worked at fostering a spirit of collectivity …
Continue reading »Fraction Talks
Discussion is one of the organic ways through which human interaction occurs, but not all discussion is created equal in the math classroom. The tone of discussion relies on the mode of listening (Davis, 1996). Most classroom talk focuses on an evaluative mode of listening. Students are expected to share, compare, and contrast solutions to problems.I do think that justification of their solutions gets at some important points regarding mathematical reasoning, but would like to move the discussion to center around that exact feature–the reasoning. Rather than piecing together the pieces of isolated reasoning (which I still think has value), I want to see a collective …
Continue reading »Conceptualizing Drills
I have students in an enriched class that demand for me to give them more practice. I tell them that we practice mathematics with daily class activities. They don’t want practice, they want repeated practice. They are accustomed to receiving repeatable drills to cement understandings. I have learned to compromise with this demand. I do believe there is a place for basic skills training in mathematics, and would raise an eyebrow at anyone who claims these unnecessary. I do, however, also believe that the heart of mathematics is problem posing, problem framing, and problem solving. Here is how I’ve infused …
Continue reading »Fraction War Task
A while ago I wrote a post on embedding atomic skills into tasks so that the basic skills are developed and used as tools of mathematics rather than the ultimate goal of mathematics. I try to develop tasks that follow this framework. I want the student to choose a pathway of thought that enables them to use basic skills, but doesn’t focus entirely on them.Recently, I was reading Young Children Reinvent Arithmetic: Implications of Piaget’s Theory by Constance Kamii and came across one of her games that she plays with first graders in her game-driven curriculum.The game was called double …
Continue reading »Fractions From Digits
This week marked my baptism by fire into the twitter world. It was not long until I was neck deep in tweets, favorites, re-tweets, and followers. The eternal nerd awoke inside me when I was confronted with my first NCTM “Problem of the Day”. A simple, yet dangerously deep, question was posed. Wanting to cement my reputation as a responsible twit, I sat down and began to tinker with the theory. The question was as follows: How many different fractions can you write using only the digits 1,2,3 & 4? Be sure to include fractions greater than 1. Immediately, I …
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