http://www.edb.utexas.edu/empson ‘See that!’ said Pippi [to the teacher]. ‘You knew it yourself. Why are you asking then?’ Sun, 25 May 2008 15:27:51 +0000 http://backend.userland.com/rss092 en In a recent Foreign Affairs article, Fareed Zakaria quotes the former Minister of Education in Singapore comparing the U.S. and Singapore's mathematics and science education: Tharman Shanmugaratnam, until recently Singapore's minister of education, explains the difference between his country's system and that of the United States: "We both have meritocracies," Shanmugaratnam ... http://www.edb.utexas.edu/empson/?p=95 What do students learn when they are taught only one way to subtract? In this discussion between two boys who are playing a trading card game and need to subtract 347 from 6000, Linda Levi muses on the things one boy learned and some opportunities involving the development of ... http://www.edb.utexas.edu/empson/?p=91 This was the question asked by Ed Silver and his colleagues at the University of Michigan in "Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom" (abstract only), published in the Journal of Mathematical Behavior. They worked with ... http://www.edb.utexas.edu/empson/?p=57 Researchers tend to agree that mid- to high-performing children benefit from instruction that emphasizes solving and discussing non-routine problems. When it comes to children who struggle, however, there is sharp disagreement and differing recommendations regarding how to teach them. Sometimes caught in a vicious cycle that requires that they know ... http://www.edb.utexas.edu/empson/?p=72 A central tenet of the mathematics education reform movement is that mathematical discourse practices such as explaining thinking, conjecturing, analyzing strategies, and justifying solutions are essential component of what it means to do and learn mathematics... There is a paucity of research, however, focusing on English Language Learners' (ELL) participation ... http://www.edb.utexas.edu/empson/?p=69 Have you gotten the email that begins, "Last week I purchased a burger at Burger King for $1.58..."? It goes on to recount the difficulty the clerk had making change for $2.08, then explains this difficulty with a humorous list of word problems through the decades that shows, supposedly, just ... http://www.edb.utexas.edu/empson/?p=68 Birmingham News has just published photos from the civil rights era that were considered too inflamatory to publish when they were taken. I was struck, in particular, by the expressions on the faces of the two young black women as they entered an all-white school for the first time and ... http://www.edb.utexas.edu/empson/?p=60 For many people, the answer is "obviously, yes." But when and how? Research on young children's mathematical thinking has shown that children can invent strategies to solve problems that are posed within their zone of understanding. Asking children to invent strategies aids the growth of understanding; how a child solves ... http://www.edb.utexas.edu/empson/?p=55 These problems and teachers' investigations of them were part of my presentation at the California Mathematics Council's recent conference in Palm Springs. 1. Jason ate 2/3 of an ice-cream sandwich. He let the rest melt. But he was still hungry, so he ate 5/6 of another ice-cream sandwich. He let ... http://www.edb.utexas.edu/empson/?p=53 I know of many districts who have responded to the increased pressures of high-stakes standardized testing by standardizing the curriculum, in some places, right down to the page number a teacher should be on for any given day. Almost all of the teachers I know realize that this kind of ... http://www.edb.utexas.edu/empson/?p=52 http://www.edb.utexas.edu/empson/?p=51 This story, a true one from a case study of a first-grade teacher's classroom, shows the power of giving a struggling child problems that he can solve and explain. Billy started first grade six weeks late, having never been to kindergarten. He couldn't count or recognize numerals. His teacher, Ms. ... http://www.edb.utexas.edu/empson/?p=49 This question is probably the one I ask the most whenever I'm working with children. (Some people who aren't children get irritated when I ask it. They take it as a sign that there is a flaw in their thinking. But usually, I'm just curious.) Today I ran across a ... http://www.edb.utexas.edu/empson/?p=50 This new study by Lubienski and Lubienski suggests the answer is a resounding, if not surprising, no. Past studies, including the most recent NAEP, have shown that private schools produce higher achievement than public schools in mathematics, even when the fact that private schools serve a different population of students ... http://www.edb.utexas.edu/empson/?p=48 In my writing about fractions, I call situations where some quantity is shared equally among some number of people "equal sharing." Many other people call these same kinds of situations "fair sharing." But, as Elizabeth Fennema once pointed out to me, "fair" does not always mean "equal." Just a couple ... http://www.edb.utexas.edu/empson/?p=47 Here's a link to a discussion of a logic puzzle, among other things, on none-other-than-RLC's blog. (He's my husband; some of the Agents in question are my children.) We all found the logic puzzle fun. http://www.edb.utexas.edu/empson/?p=45 Linda Jaslow has been working on fractions in a first-grade classroom using equal sharing problems. She sent this description of one girl's insight about how to generate equivalent fractions: We also had an amazing revelation by a first grader on equivalent fractions. The class had done a great deal of ... http://www.edb.utexas.edu/empson/?p=44 My two sons know that because I am a math educator, I like to give them problems to solve every once in a while. Last year, when they were first and third graders, I drew a picture of a brownie that had been cut with a slice removed and asked ... http://www.edb.utexas.edu/empson/?p=43 Luz Maldonado and I worked with four second graders who were having difficulties in math, for about 10 weeks. Each of us got together with them once a week, on separate days. What follows are my reflections on working with these four children. As you will see, our work soon ... http://www.edb.utexas.edu/empson/?p=20 Today I wrote a mix of problems for the children to solve that would give us some insight into what the children had learned about base-10 concepts and their use in problem solving. I worked with Jack and Sunny, and Luz worked with Emilio and Daniella. Jack. Jack seems to have ... http://www.edb.utexas.edu/empson/?p=39