tag:blogger.com,1999:blog-1907702537884089718.post8601746975656913634..comments2017-04-27T18:45:03.512-07:00Comments on Exit 10A: Ball Don't LieJoe Schwartznoreply@blogger.comBlogger9125tag:blogger.com,1999:blog-1907702537884089718.post-34931918775346718402017-02-15T03:30:13.884-08:002017-02-15T03:30:13.884-08:00Thanks so much for your observations and for shari...Thanks so much for your observations and for sharing your experiences. I like your comment that, "Starting change from yourself is always the way." When I get frustrated or upset about the state of affairs in math education I have to remind myself that it took a very long time for things to get this way, and it could take a long time for things to change. But I have faith that things will change, one teacher at a time, one student at a time, one classroom at a time. Joe Schwartzhttp://www.blogger.com/profile/11524614672307520366noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-49180810601561066692017-02-13T06:26:41.136-08:002017-02-13T06:26:41.136-08:00I think there is also a lot of emphasis on hard ev...I think there is also a lot of emphasis on hard evidence in the system. The perception of students, parents and oftentimes teachers is that the evidence of doing math has more value than the flimsy evidence of flimsy understanding. I was once told at the parent conference that no one cares about understanding, it will eventually come one day, or if not no one still cares. People in my province were protesting at the legislature that they want "back to basics"math back. Many students in my community are enrolled in worksheet-based tutoring systems that skip the understanding part all together.<br />Hanging around MTBoS, I sometimes forget that people on my twitter feed still don't represent status quo in how the discipline of mathematics is perceived.<br />But there is no sense in complaining about the system, starting change from yourself is always the way.<br />Thank you for your post.TAnnalethttp://www.blogger.com/profile/02611816015421905358noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-81077538077288302262017-02-02T10:35:04.631-08:002017-02-02T10:35:04.631-08:00I wish that we placed more emphasis on diagnostic ...I wish that we placed more emphasis on diagnostic interviews. Believe it or not, for us it's all paper and pencil from grade 1 on. I know this is well covered ground, but the reading people place so much emphasis on their running records, and we don't have anything comparable. So teachers are left to their own devices and rely on the paper and pencil, sometimes because they don't know what questions to ask or what to even look or listen for. Joe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-52448891678877738992017-02-02T10:26:28.137-08:002017-02-02T10:26:28.137-08:00Thanks for steering me to Denise's fraction ga...Thanks for steering me to Denise's fraction game. I really like the way you used it as a formative assessment. I wonder how surprised the teacher who assured you that the students "understood fractions" was. The way you re-ordered the targets makes sense to me. I could see some students lingering at beginning targets while others move on to the later ones. I will give your posts a close read and look forward to trying this out with our students. And I think I'm also going to modify this to use with whole numbers.Joe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-53114642371094505912017-02-02T10:19:03.382-08:002017-02-02T10:19:03.382-08:00Thanks for your comments, Jill. I agree with you ...Thanks for your comments, Jill. I agree with you about the connection between well designed tasks and sense-making. I think a really good example of that is what Joshua Greene describes in his comment below. Joe Schwartzhttp://www.blogger.com/profile/02304083254248927187noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-80339802258556713842017-02-02T06:26:16.880-08:002017-02-02T06:26:16.880-08:00This is exactly why I show the teachers I work wit...This is exactly why I show the teachers I work with the Cathy Humphries/Ruth Parker book Making Number Talks Matter. In this resource they have number talks that work specifically on building students fraction sense. Looking at two fractions and comparing them based on benchmarks of 0.1/2,1 and 2. I also love the one where they have you place two fractions on the board and ask the students if they were to add these two fractions would the answer be closer to 0.1/2,1 or 2. These number talks help build fraction sense so well! Throw in some fractiontalks.com and you are away. Your posts also reminds me of why diagnostic interviews are so important from collecting assessment data through conversation, observation and product. Ontario has now made those three weighted the same in our collection of assessment data, unfortunately we still see product being used the most especially in junior/intermediate grades. Thanks for sharing Joe.Mark Stamphttp://www.blogger.com/profile/08283291764124745874noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-81020030886093797482017-02-02T03:28:07.192-08:002017-02-02T03:28:07.192-08:00I cried.I cried.Howard Phillipshttp://www.blogger.com/profile/18297158336334346872noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-35826798254380839682017-02-01T22:04:03.886-08:002017-02-01T22:04:03.886-08:00I spent the last three weeks (one hour per week) p...I spent the last three weeks (one hour per week) playing a fraction comparison game (from <a href="https://denisegaskins.com/2014/08/06/fraction-game-my-closest-neighbor/" rel="nofollow">Denise Gaskins</a>) with a 4th grade class and some one-on-one time with two younger students. This game was really effective at distinguishing levels of understanding:<br />(0) some kids are totally at sea. They don't really understand what this a/b thing means, how a and b are related, etc. These kids struggle with the first round of the game when the target is 0, when the idea is to just want to make their fraction as small as possible.<br />(1) Some kids have got a basic understanding of the meaning of the fraction and can play confidently when the target is 0 or 1. They might still be weak about equivalent fractions. Trying to play some spot-on equivalents when 1/3 and 1/2 are targets is a give-away.<br />(2) familiar with some frequent friends: kids who can tell readily whether their plays are larger or smaller than the target for 1/3, 1/2, 3/4.<br />(3) proficient: have at least one consistent strategy they can work through to make a comparison<br />(4) fraction black-belts: using multiple strategies, already familiar with many of the most common comparisons.<br /><br />I don't know precisely what fraction experience the 4th graders had, but their teacher assured me that "they understand fractions." In that class, I saw kids at stages 0-4.<br /><br />The younger students had a very sound foundation in models of fractions: diagrams of pies, cakes, chocolate bars, number lines and physical experience with baking measures and fractional inches on measuring tapes and rulers. They were also introduced to and practiced four methods for comparing fractions:<br />(1) common denominators<br />(2) common numerators<br />(3) distance to 1<br />(4) relationship to another benchmark number. Like 1/2 in your 4/6 and 8/18 example, a "familiar friend" that should be relatively easy to see it is larger than one and smaller than another. In practice, 1/2 seems to be the most popular benchmark.<br /><br />Not surprisingly, they were the only ones at/approaching stage 5.<br /><br />I wrote up notes in a couple of blog posts: <a href="http://3jlearneng.blogspot.com/2017/01/my-closest-neighbor-fraction-game.html" rel="nofollow">4th grade class</a>, <a href="http://3jlearneng.blogspot.com/2017/01/closest-neighbor-one-on-one.html" rel="nofollow">one-on-one</a>.<br /><br />Other than the ideas I listed in my post, I would make other changes for the whole class activity (a) lean toward doing this more as a cooperative puzzle, (b) re-order the targets for the rounds as 0, 1, 1/2, 3/4, 1/3, 2 and (c) I also would consider allowing equivalent fractions to the target as winning plays.Joshua Greenehttp://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-1907702537884089718.post-39981191664214530362017-02-01T18:11:01.378-08:002017-02-01T18:11:01.378-08:00Thank you for this post. My love for fractions is...Thank you for this post. My love for fractions is uncontrollable but only since I've become a teacher. The amount of sensemaking that can happen in a well thought out fractions lesson/task is mind blowing (for me and for students!Teacher Jillhttp://www.blogger.com/profile/04463419707555471060noreply@blogger.com