tag:blogger.com,1999:blog-18655328936438121612024-03-23T06:13:24.316-04:00Middle School Math Moments (now Cognitive Cardio Math)As a middle school teacher, there are many moments to reflect upon. This blog will be a place to reflect upon all of those moments (and more)!Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.comBlogger233125tag:blogger.com,1999:blog-1865532893643812161.post-26483884989948605112016-11-15T22:32:00.003-05:002024-01-19T11:28:07.108-05:00How to Check Your Math Work: Suggestions for Students<div class="separator" style="clear: both; text-align: center;">
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This post has been moved to <a href="https://cognitivecardiomath.com/cognitive-cardio-blog/helping-students-learn-how-to-check-math-work/">cognitivecardiomath.com</a><br />
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<br />Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-79791595035738507302016-11-10T11:49:00.000-05:002016-11-11T12:28:01.560-05:00Help Students Learn to Manage Their Time<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDqppVQQl9upnGZRHzjraoGCLUEk3GBHgwpTeVeMoSyVO96g7pHBkVgdx6bMKfUgWmQMmHQ-VrGGclTZtiocnq1dNA6AHFU4HPIEKc-45i_NWB10iHav03SNF97kj8PFqW6Im2s0Z3SCLz/s1600/Slide1.GIF" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDqppVQQl9upnGZRHzjraoGCLUEk3GBHgwpTeVeMoSyVO96g7pHBkVgdx6bMKfUgWmQMmHQ-VrGGclTZtiocnq1dNA6AHFU4HPIEKc-45i_NWB10iHav03SNF97kj8PFqW6Im2s0Z3SCLz/s400/Slide1.GIF" width="266" /></a></div>
In my early years of teaching, I didn't always know what to say when students told me they didn't have time to do their homework (other than something like, "You must have had some time between 4:00 and 9:00!). There were all kinds of reasons - they had sports practice or a lesson, or they had to go to their brother's or sister's game/practice/event of some kind; or their parents took them shopping or out to eat. At that time I had one child (who was 2 when I started teaching), so I didn't have the experience from a parent's point of view of making sure I was getting my kids to their activities, getting done all the house-related things, and also making sure they were getting their homework done. This made it a little difficult for me to relate to the students' situations, but I tried to help them think about how much time they <i>did </i>have to do their work.<br />
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Being involved in activities definitely reduces time for schoolwork, but it doesn't mean that schoolwork can't get done. Students can learn to manage their time, but they need to be shown how. There are many of us who, as adults, may not manage our time very well. And if a parent is not great at managing time, how will he or she teach their children to manage theirs? Even when adults <i>are</i> good at managing time, they don't always think to teach their children how to do what they do.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXsE1mCd6-hdmy3pzzTD4oeW7cOcXoJbRU0OgkoQ2PKkoUnwYJpB97A6Dzl3_crHNqmufHggSVXByJxMJZl7CzP9rpArOdPYWZh194nCNbqF215w0F_WDquhwzAGk-qptJoFijydhB9_3V/s1600/Slide2.GIF" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXsE1mCd6-hdmy3pzzTD4oeW7cOcXoJbRU0OgkoQ2PKkoUnwYJpB97A6Dzl3_crHNqmufHggSVXByJxMJZl7CzP9rpArOdPYWZh194nCNbqF215w0F_WDquhwzAGk-qptJoFijydhB9_3V/s400/Slide2.GIF" width="400" /></a>Because their parents might not talk about time management, I've spent many years teaching students (5th and 6th graders) how to find their available work time. I make
these planner-type pages and have students fill in a sample week,
so they can see where their available time is. When they fill in the
practices, games, lessons, sibling practices, etc, they can then see
what time is left in the day. If homework is assigned Monday and brother
has practice, the student can see that they have a chunk of time from
3:30-6:00 (when they probably also eat dinner) and then 8-9:00. If homework completion can fit in those time slots, great! They can plan to use that time wisely. If it's not enough time, then they need to use another strategy to get things done. One of the fun parts of using the calendar/planner is the color-coding! When I used this for my own planning, I
color-coded according to person (my son was green, oldest daughter
orange, youngest purple, and I was blue:-). <br />
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If their chunks of time aren't big enough, students need to find other ways to complete their work. One of the strategies I share with students is to take backpacks and homework supplies in the car with them. When one of my three children had practice (they're all beyond this point now), the others brought any work they had to do. Sometimes homework was completed sitting on a blanket in the grass or sitting in the bleachers. Sometimes it was completed in the car while we waited. Do distractions occur when homework is done this way? Yes, they sometimes do. But, to me, using that time to work was better than losing an hour or two (or more, depending on travel time!) and then having to do everything after we got home (especially if we still had to have dinner!)<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirMP7EZ08rRCynUFbpRxNtH9Ptb4DJwpHtVny8ZhPVJUIXy2GnZHyAQwytelsBrBAEWjF4QbWdtdu9NXNfnenIMFqeRJQr7hlGPXNqV2z7WO1NeQklr22QvMUQ2poPrIpON1ueHv78M9qM/s1600/Slide1.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirMP7EZ08rRCynUFbpRxNtH9Ptb4DJwpHtVny8ZhPVJUIXy2GnZHyAQwytelsBrBAEWjF4QbWdtdu9NXNfnenIMFqeRJQr7hlGPXNqV2z7WO1NeQklr22QvMUQ2poPrIpON1ueHv78M9qM/s320/Slide1.JPG" width="320" /></a>I also suggest that students try to study while they're driving to an event. They can read over notes and quiz themselves. If there are several people in the car, one person can quiz another. The student can quiz their parent as well, or explain information to mom or dad....this is a great way for a student to be sure his knowledge is solid.<br />
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I always suggest that students put upcoming tests on their calendars and then work backwards to schedule their study time....so they could label the driving time as study time. Projects should go on the calendar too, so students can again work backwards to fit in the necessary time to complete them.<br />
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The great thing about a week at a glance like this is that students don't have to depend on someone buying them a planner or printing out pages for them. They can write out their own schedule on their own paper and design it any way they'd like. Then they can post in it their room, on the frig, or keep it in a school binder.<br />
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As I mentioned, in the early days, I didn't quite know how to respond to students who didn't have time to do their work. But now, this is something I teach every year, to help avoid those "I didn't have time because...." statements :-)<br />
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<br />Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-15505677973234943992016-10-23T21:23:00.002-04:002024-01-19T11:35:34.104-05:00Fall Freebie!<div style="text-align: center;">
Hard to believe that we're approaching the end of October!!</div>
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I made this cross number puzzle to use with fast finishers over the next couple of weeks:-)</div>
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Hope you can use it!</div>
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<tr><td class="tr-caption" style="text-align: center;"><a href="https://cognitivecardiomath.com/cognitive-cardio-blog/engaging-fall-activities-for-middle-school/">Click to access on new site</a></td><td class="tr-caption" style="text-align: center;"> </td><td class="tr-caption" style="text-align: center;"> </td><td class="tr-caption" style="text-align: center;"> </td></tr>
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<br /><br />Have a great week!<br />
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<br /><br />Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-75525453522689850442016-10-14T12:24:00.006-04:002024-01-19T11:04:24.873-05:00Problem of the Week, #14<div style="text-align: center;">
All problems can now be found here, on my new site: </div><div style="text-align: center;"><a href="https://cognitivecardiomath.com/free-resource-center/">https://cognitivecardiomath.com/free-resource-center/</a><br />
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This one's a quick Halloween-themed logic puzzle. I hope you can use it!</div>
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All problems are now on my new site: <a href="https://cognitivecardiomath.com/free-resource-center/">https://cognitivecardiomath.com/free-resource-center/</a><br />
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Time for Problem of the Week, #13!</div>
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Part A of this week's problem asks students to write an algebraic equation for a situation (students will need to use 2 variables). In Parts B and C, they need to substitute the given information into their equation to solve. </div>
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An extension for students who finish early - ask them to "create" a bracelet that will cost a specific dollar amount.</div><div style="text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNKwdWSR5f1hXtUIq8A5_sv6dvCbb1moxgLwlQVGi3e9sFkwRYbC8HNEVSwV2HGY3HGzK_NWPAGGPe08LnUdcmyzrdh5nyeCQpqpkon82yF6nD9kgBHI3NQV-OoTuAjTJIemp5ZaIKCAyLLfR4f-7wCunVNesa8IDjVu23trdPDbERwCT8sQAsbCKF3rbv/s960/problem-of-the-week-cognitive-cardio-middle-school-math%20(25).JPG" style="margin-left: 1em; margin-right: 1em;"><img alt="problem of the week cognitive cardio math (middle school math moments)" border="0" data-original-height="960" data-original-width="960" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNKwdWSR5f1hXtUIq8A5_sv6dvCbb1moxgLwlQVGi3e9sFkwRYbC8HNEVSwV2HGY3HGzK_NWPAGGPe08LnUdcmyzrdh5nyeCQpqpkon82yF6nD9kgBHI3NQV-OoTuAjTJIemp5ZaIKCAyLLfR4f-7wCunVNesa8IDjVu23trdPDbERwCT8sQAsbCKF3rbv/w320-h320/problem-of-the-week-cognitive-cardio-middle-school-math%20(25).JPG" title="problem of the week cognitive cardio math (middle school math moments)" width="320" /></a></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td class="tr-caption"><a href="https://cognitivecardiomath.com/free-resource-center/">Click here to access.</a><br /><br /></td></tr></tbody></table><div style="text-align: center;"><br /></div>
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To access all of the past Problem of the Weeks, click <a href="https://cognitivecardiomath.com/free-resource-center/">here</a>!
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Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-24633675144366520412016-09-25T19:28:00.001-04:002016-09-25T19:28:43.196-04:00#MathDates for 9/26 - 9/30<div style="text-align: center;">
In case you haven't found these on Instagram or Facebook, here are the dates as mathematical expressions for the coming week:-)<br />
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</div>Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-69191108019704864942016-09-18T18:43:00.002-04:002016-09-18T18:43:22.402-04:00Math Dates 9/19-9/23/16<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcgDkurMAwZ6U-SREuXz8hl4Z0QDFgFopfIeN2_LvFqa80G8xz_fif7Uuzl1-r4mVQPekDQMCBvwDQC5650zgrYs7N_CQYM-MxcYAzUjDpCZnblpPIwSRkgjESY2LgYWEnF8t1KZspIyS9/s1600/%2523mathdates+9.18.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcgDkurMAwZ6U-SREuXz8hl4Z0QDFgFopfIeN2_LvFqa80G8xz_fif7Uuzl1-r4mVQPekDQMCBvwDQC5650zgrYs7N_CQYM-MxcYAzUjDpCZnblpPIwSRkgjESY2LgYWEnF8t1KZspIyS9/s640/%2523mathdates+9.18.jpg" width="480" /></a>This week's math dates are pictured here!<br />
If you've been using the math dates for a few weeks, this week might be a good week to make a "mistake" in one of the days and see if your students notice - keep them on their toes!<br />
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I included several fractions with exponents in both the numerator and denominator this week. If your students aren't familiar with exponent rules, they might make some observations and discover a rule for themselves by the end of the week:-)<br />
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If you have trouble reading the dates here on the blog, you can also find them on my <a href="https://www.instagram.com/middleschoolmathmoments/">Instagram</a> and <a href="https://www.facebook.com/middleschoolmathmoments">Facebook</a> accounts.<br />
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Have a great week!<br />
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Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-26322331408017096652016-09-16T14:33:00.000-04:002017-03-05T22:18:56.266-05:00How Can You Help Change a Negative Math Mindset?<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghyqYKnVBsSA0TyeSnL9dj5PvrfdyCjy3fco2tV4Eh1h04J4FTOC3o9WNNXxtDKjpjPvbatALl0bqz5s-K902OgWgpyqydTjTQXDCmM6dwfrLTFxpPuSD7RilPJUBkXmqlX_z8dNoH2_2X/s1600/Help+change+a+negative+math+mindset.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghyqYKnVBsSA0TyeSnL9dj5PvrfdyCjy3fco2tV4Eh1h04J4FTOC3o9WNNXxtDKjpjPvbatALl0bqz5s-K902OgWgpyqydTjTQXDCmM6dwfrLTFxpPuSD7RilPJUBkXmqlX_z8dNoH2_2X/s400/Help+change+a+negative+math+mindset.jpg" width="308" /></a><span style="font-family: century gothic;">This post has been moved to: <a href="http://www.cognitivecardiowithmsmm.com/blog/how-can-you-help-change-a-negative-math-mindset">http://www.cognitivecardiowithmsmm.com/blog/how-can-you-help-change-a-negative-math-mindset</a></span><br />
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This post has been moved to: <a href="http://www.cognitivecardiowithmsmm.com/blog/integers-fold-it-up-freebie">http://www.cognitivecardiowithmsmm.com/blog/integers-fold-it-up-freebie</a><br />
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Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-63886582855076366452016-07-31T09:15:00.001-04:002017-03-12T21:03:47.033-04:00Fun with Math Dates, 2016-17Math Dates can now be found at: <a href="http://www.cognitivecardiowithmsmm.com/math-dates.html">http://www.cognitivecardiowithmsmm.com/math-dates.html</a><br />
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It's almost August! I'm always amazed at how quickly the time goes!<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSZSZrTZcMHXnascnIvA4QZMioPhN9VSEBBAOxf7x9Pm4bTx6Arw4AAe5DUY6iunWVTul6_V0h9VQxTTDsMUqNs6CxVvOg-vjomZizK8aNlRZz6cFVEagU1GeBBirLTFxlLiM9jfftDMSx/s1600/dates+7.25.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSZSZrTZcMHXnascnIvA4QZMioPhN9VSEBBAOxf7x9Pm4bTx6Arw4AAe5DUY6iunWVTul6_V0h9VQxTTDsMUqNs6CxVvOg-vjomZizK8aNlRZz6cFVEagU1GeBBirLTFxlLiM9jfftDMSx/s320/dates+7.25.jpg" width="260" /></a>This is just a quick post to share what I'm planning with "math dates" this year. Last year, I got such a positive response when I posted ways to write the dates as mathematical expressions. So I decided to get a little more organized with it this year, and plan the week of dates on Sundays, instead of thinking of them one day at a time.<br />
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Every Sunday, I'm going to post the week's dates on <a href="https://www.instagram.com/middleschoolmathmoments/" target="_blank">Instagram</a> and <a href="https://www.facebook.com/middleschoolmathmoments" target="_blank">Facebook</a>, so if you'd like to use them, you might want to follow me one of those platforms (if you aren't already). I'll post the dates here sometimes as well, but not as regularly.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRdV9n9Hh440yS8Rc6gUNgBoerwuskvTfxJZ3r8EBX6uQP_sZkt2A0wju8Hm-x3yE3lQclw5FCcsFt2jFZJlKEqzT-HyA0pymnhDdo0sbYcxKcLT4Bex4yQal0F3LiMhGVxBOstlA212b/s1600/dates+8.1.16.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxRdV9n9Hh440yS8Rc6gUNgBoerwuskvTfxJZ3r8EBX6uQP_sZkt2A0wju8Hm-x3yE3lQclw5FCcsFt2jFZJlKEqzT-HyA0pymnhDdo0sbYcxKcLT4Bex4yQal0F3LiMhGVxBOstlA212b/s320/dates+8.1.16.jpg" width="260" /></a>I loved using expressions as the dates last year - it kept students fresh with their exponents/exponent rules, exposed them to roots (we don't really study these yet in 6th grade), and encouraged them to figure out their own expressions. <br />
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Do you already use something like this in your classroom?<br />
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**Fonts in images by <a href="https://www.teacherspayteachers.com/Store/Kimberly-Geswein-Fonts" target="_blank">KG Fonts</a>Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-90279223573114268592016-07-24T08:07:00.002-04:002017-12-10T14:19:03.416-05:00WHY the Butterfly Method When Adding and Subtracting Fractions?<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbvMm6YkV4uO0qpyqzDMa-XJi9uzDAFg13fcfernW8A08vTqluiUjpU0V3XFMBrnZF8Ay5wVhKigoXBI950ZXLdbuxj4A1kjc-lPKwvUowKB60UTPFLGabkf77doxIRxppU-2ZGHqEQTeK/s1600/butterfly+why+500.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbvMm6YkV4uO0qpyqzDMa-XJi9uzDAFg13fcfernW8A08vTqluiUjpU0V3XFMBrnZF8Ay5wVhKigoXBI950ZXLdbuxj4A1kjc-lPKwvUowKB60UTPFLGabkf77doxIRxppU-2ZGHqEQTeK/s400/butterfly+why+500.jpg" width="400" /></a><br />
This post is also found at: <a href="http://www.cognitivecardiowithmsmm.com/blog/why-the-butterfly-method-when-adding-and-subtracting-fractions">http://www.cognitivecardiowithmsmm.com/blog/why-the-butterfly-method-when-adding-and-subtracting-fractions</a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG9_TS3iCuFUPsS_t96gmngztSl9ftWZgJm1_LrIzVWai0yPU3pmjlI-dOrG1lf2YtNGm5pdfnxdC5oMFrTvzDjlpRz6cl384g7nzceKQVfwKbL_vswis5_oKEcD_N-VLc_46uPN0BQYH3/s1600/math+and+ping+pong+pic.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG9_TS3iCuFUPsS_t96gmngztSl9ftWZgJm1_LrIzVWai0yPU3pmjlI-dOrG1lf2YtNGm5pdfnxdC5oMFrTvzDjlpRz6cl384g7nzceKQVfwKbL_vswis5_oKEcD_N-VLc_46uPN0BQYH3/s320/math+and+ping+pong+pic.jpg" width="272" /></a></div>
This post has been moved to <a href="http://www.cognitivecardiowithmsmm.com/blog/math-and-ping-pong">http://www.cognitivecardiowithmsmm.com/blog/math-and-ping-pong</a><br />
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**Fonts in graphic by <a href="https://www.teacherspayteachers.com/Store/Kimberly-Geswein-Fonts" target="_blank">KG Fonts</a>Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-23509913486579326142016-07-02T11:21:00.001-04:002017-12-10T14:20:41.563-05:00Fraction Division - Another Way?<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiglUaoExaBP-9Kh6Isjjv9UQfWr_KYOZ7u950umY6GoL0yz9WGxkw9k5bHhZrbVFKrF5-yLxkbodEbBGYJ8zBpfTANblF9xEE-WVi7xw9vadqvS61bk9LOCncSTAPMsa0D2DWkbyyeyE3c/s1600/fraction+division+pin+pic.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiglUaoExaBP-9Kh6Isjjv9UQfWr_KYOZ7u950umY6GoL0yz9WGxkw9k5bHhZrbVFKrF5-yLxkbodEbBGYJ8zBpfTANblF9xEE-WVi7xw9vadqvS61bk9LOCncSTAPMsa0D2DWkbyyeyE3c/s400/fraction+division+pin+pic.jpg" width="266" /></a><br />
This post has been moved to: <a href="http://www.cognitivecardiowithmsmm.com/blog/fraction-divisionanother-way">http://www.cognitivecardiowithmsmm.com/blog/fraction-divisionanother-way</a><br />
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<br />Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-55535098580377309672016-04-23T23:06:00.003-04:002017-12-10T14:21:59.603-05:00Focus & Fun with the Array Game, Using Polyhedral Dice<a href="http://www.amazon.com/gp/product/0470894520/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0470894520&linkCode=as2&tag=midschmatmoma-20&linkId=ROJ4XWQD4VQO2HWP" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0470894520&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=midschmatmoma-20" /></a><br />
This post has been moved to: <a href="http://www.cognitivecardiowithmsmm.com/blog/focus-fun-with-the-array-game-using-polyhedral-dice">http://www.cognitivecardiowithmsmm.com/blog/focus-fun-with-the-array-game-using-polyhedral-dice</a><br />
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<br />Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-81897678758071336172016-03-25T08:38:00.001-04:002017-02-27T20:42:45.536-05:00Playing "Decimal Dice" - Converting Fractions to DecimalsThis post has been moved to: <a href="http://www.cognitivecardiowithmsmm.com/blog/playing-decimal-dice-converting-fractions-to-decimals">http://www.cognitivecardiowithmsmm.com/blog/playing-decimal-dice-converting-fractions-to-decimals</a><br />
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<span style="font-family: "verdana" , sans-serif;"><span style="font-size: large;"><span style="color: black;"></span></span></span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-fQjlFUNl7lesiCMKFlLv4w4Ds9RJD3kuwNzdHzXAIl_LumLX1krXLrwcsievMtKaWSqtjmlQW_VnhXkyFoqY9wCH6PMvtgUByvOOurNBqSPDuXm0nvTu4tQJW0h-CLyKh5kqM1dQXGmn/s1600/decimal+dice+example+3+pic.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Check out this decimal dice game to help students practice converting fractions to decimals!" border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-fQjlFUNl7lesiCMKFlLv4w4Ds9RJD3kuwNzdHzXAIl_LumLX1krXLrwcsievMtKaWSqtjmlQW_VnhXkyFoqY9wCH6PMvtgUByvOOurNBqSPDuXm0nvTu4tQJW0h-CLyKh5kqM1dQXGmn/s400/decimal+dice+example+3+pic.jpg" title="Playing decimal dice" width="300" /></a></div>
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<!--End mc_embed_signup-->Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-29104744436584537112016-03-14T05:33:00.002-04:002024-01-19T11:09:33.176-05:00Ratios and Proportions Problem Solving - Problem of the Week 11<div style="text-align: center;">All problems are now on my new site: <a href="https://cognitivecardiomath.com/free-resource-center/">https://cognitivecardiomath.com/free-resource-center/</a><br /></div>
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Happy Monday!<br />
It's a rainy Monday here this morning....and a bit darker than usual with the time change, so I really wanted to stay in bed today! <br />
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We are working with ratios and proportions in 6th grade math this week, SO this week's problem of the week is a pizza-themed ratio problem solving activity.<br />
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I hope you can use it! You can click below to access:-)<br />
Have a great day!<div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjCHK2CcUN7tQSTpaWJMEIKxPOpuxb2q5W5bYCjkppAIh4R0yzNV5NNooZpPH2x7Wgaplm3qZDsrMFrjR83dTzaDBXsXO1PmnoFyArSuxCe6guwfNGUr6Gq5KidqQQRNoemQk6UFUcnRiEYGp2Eh7-aHs3BI6ekFdOvhRwS1XONNSI3oHaeQurIYK3Exal/s960/problem-of-the-week-cognitive-cardio-middle-school-math%20(23).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="problem of the week cognitive cardio math (middle school math moments)" border="0" data-original-height="960" data-original-width="960" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjCHK2CcUN7tQSTpaWJMEIKxPOpuxb2q5W5bYCjkppAIh4R0yzNV5NNooZpPH2x7Wgaplm3qZDsrMFrjR83dTzaDBXsXO1PmnoFyArSuxCe6guwfNGUr6Gq5KidqQQRNoemQk6UFUcnRiEYGp2Eh7-aHs3BI6ekFdOvhRwS1XONNSI3oHaeQurIYK3Exal/w200-h200/problem-of-the-week-cognitive-cardio-middle-school-math%20(23).JPG" title="problem of the week cognitive cardio math (middle school math moments)" width="200" /></a></div><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0 0 0 40px; padding: 0px;"><blockquote style="border: none; margin: 0px 0px 0px 40px; padding: 0px; text-align: left;"><a href="https://cognitivecardiomath.com/free-resource-center/" style="text-align: center;">Click to access</a></blockquote></blockquote></blockquote></blockquote></blockquote></blockquote></blockquote><div><br /><br />
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To access all of the Problem of the Weeks, click <a href="https://cognitivecardiomath.com/free-resource-center/">here</a>!<br />
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This post has been moved to: <a href="http://www.cognitivecardiowithmsmm.com/blog/fun-with-math-dates" target="_blank">http://www.cognitivecardiowithmsmm.com/blog/fun-with-math-dates</a></div>
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<!--End mc_embed_signup-->Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-47283377932011834532016-01-31T16:37:00.000-05:002016-03-25T08:46:02.574-04:00What's Math Got To Do With It? Chapter 5Chapter 5: Stuck in the Slow Lane: How American Grouping
Systems Perpetuate Low Achievement
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimaWny1SM3ZfVe86bAPlOPa8bDBeh248ntIEPTy4jaXkYCpGkUW-PDqMn3plyBXe3qWWKgcAXZ33PDxiT4WeXTMcUNp7cd7PEleRhhBnrzrSmBs9JO40dHshOZrip255m1h0d04jjNHHgP/s1600/ability+group.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="What's Math Got to Do With It? by Jo Boaler" border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimaWny1SM3ZfVe86bAPlOPa8bDBeh248ntIEPTy4jaXkYCpGkUW-PDqMn3plyBXe3qWWKgcAXZ33PDxiT4WeXTMcUNp7cd7PEleRhhBnrzrSmBs9JO40dHshOZrip255m1h0d04jjNHHgP/s320/ability+group.png" title="What's Math Got to Do With It? by Jo Boaler" width="320" /></a>Wow, what a chapter. This one has made me rethink some of my
beliefs. Most of my 24 years of teaching math has included grouping by ability. It
was such a big push in my early years of teaching – our smaller elementary school didn’t
group, but one of the bigger elementary schools did, and the parents pushed for
(and got) “equity” among the schools. So we all started grouping. <span style="mso-spacerun: yes;"></span>Ability-grouping has become ingrained, so reading (in
this chapter) that ability grouping is <i style="mso-bidi-font-style: normal;">illegal
</i>in some countries in the world, including Finland (at the top in
international achievement tests), really surprised me. Grouping is banned because when students are put in lower ability
classes, they receive lower-level work, which Boaler says is damaging and
suppresses achievement. Non-ability grouping provides more students with the opportunity
to learn – which is needed in order to achieve. Makes sense.</div>
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Boaler states that in the US, students are typically grouped around 7<sup>th</sup>/8<sup>th</sup>
grade. (In past years, our district has been grouping as early as 2<sup>nd</sup> grade....)</div>
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This chapter shares research results that support the idea that grouping in math is not the best approach for student achievement.</div>
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As Boaler states at the start of this chapter – parents want
ability grouping because they want their “high-achieving, motivated children to
be working with similar children.” Boaler shares that international studies
reveal high-performing countries like Japan and Finland reject ability
grouping. The countries that use ability grouping, like the US, are least successful
in math.</div>
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Results collected about eight-graders from 38 different countries showed that the US had the most tracking (US was in 19<sup>th</sup>
place), while Korea (highest-achieving country) had the least tracking and most
equal grouping. US had the strongest link between achievement and socioeconomic
success, which has also been attributed to tracking. Researchers concluded that countries that leave grouping to the
latest possible moment or use the least amount of ability grouping are the
highest achieving.</div>
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According to research, when students are not grouped by
ability, it helps not just the students who would be on the lower tracks, but
also the students who would be on the <i>higher</i> tracks. In mixed-ability classes, there are more occurrences of <i>students</i> helping
other students (rather than just teacher helping students). This helps the higher students, because explaining concepts helps them learn the concepts more deeply;
it also helps them find their own weaknesses - if they can’t explain, they
know
where they need to work. Results from one of Boaler’s studies showed that after 3
years of ability-grouped classes, students achieved at significantly lower
levels than students who had been in mixed-ability groups. “High” students felt
unable to say that they didn’t understand the work, which moved “too fast.” </div>
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<a href="https://blogger.googleusercontent.com/img/proxy/AVvXsEiI5U3uiA0RjGfMpznSqkIL5CI7I-R8bWvk2LjmsSSyS2lJGvDM8fx2WQj1eI6lFLs2LYV1QYyGpY9pJmFab8fjoFLV6ulImt-DdulDf0cG4bxE-kWgIKUPGrYlsgNNTt6zJrYoT8SPPIC453awOwSglpsKMZtFI9Hvl2ekYPxb0PFrIZXtddv87REihLawO-VlgqyYMvX32PqQ_PHhDHfzkiSPHEKbk9Jyz4CVaOExbeoIXLZFaSzDJ3nKlZryyOMhtf8NQOzroRLN0tK8vKCmruG7-cpmoxL-_EaLJ1HBDjycisE3zLye=" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="What's Math Got to Do With It? by Jo Boaler" border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0143128299&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=midschmatmoma-20" height="320" title="What's Math Got to Do With It? by Jo Boaler" width="209" /></a>In one California high school, all students started with algebra, taking 90 minute
classes for ½ year. This gave students the opportunity to take 8 math classes through high school. By the end of high school, 47%
of students took calculus and precalculus, compared to 28% of students in a typical
tracked high school. It was noted the "highest students" at the "detracked" high school achieved at higher levels than
high students in high tracks at other high schools.</div>
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Boaler shares the belief that tracking leads to a fixed mindset – the belief that “ability” is fixed. For
“high” students, being put in a high track led them to believe they were smart. According to the growth/fixed mindset philosophy, this belief sets them up to become fearful of making mistakes and avoid more
challenging work<span style="mso-spacerun: yes;">. Boaler states that this has</span> especially
devastating consequences for high-achieving girls.</div>
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Students in tracked classes are often treated as if they all
have the same needs and work at same pace, which is not true.<span style="mso-spacerun: yes;"> </span>When students are <i>not</i> grouped, there is a greater perceived need for the teacher to
differentiate both instruction and work. This results in a better match of pace and level.</div>
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In research in US
classes, it was found that tracked students tend to develop ideas about their own
potential, but also about others – as dumb or smart, quick or slow. Students in mixed-ability classes were more respectful and learned to respect different
ways of thinking.</div>
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According to Boaler, there are two critical components for mixed-ability grouping – </div>
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1) Students must be given open work that can be accessed at
different levels and taken to different levels. Teachers need to provide problems that
will be challenging in different ways, not problems that target small, specific
pieces of content. Students will learn different things at different levels
with these types of problems.</div>
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2) Students must be taught to work respectfully with each
other.</div>
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At the end of the chapter, Boaler shares that she interviewed students that had been part of studies eight years earlier. Now,
as young adults, those who had been in mixed-ability groups were in more
professional jobs that those who had been tracked.</div>
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Very interesting chapter! So much to think about.</div>
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At this point, my grade level does not group by ability, but students <i>were</i> grouped for years before coming to me...<br />
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Does your school/district use ability-grouping in math? </div>
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All problems are now on my new site: <a href="https://cognitivecardiomath.com/free-resource-center/">https://cognitivecardiomath.com/free-resource-center/</a></div>
<div>
<br /></div>
In honor of Winter Storm Jonas, this week's problem solving uses some snowfall data. This is a quick one - students use the data to find mean, median and mode. It's nice that the numbers are decimals - provides some decimal adding and dividing practice!<div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQof5GA3vQJKvDt8gvDl69rnw9A9KZf6_phSgbpU_bYwEnlEVWrqCuzMRo9norn34FL1gWIcWDCu8RSIiMHVf1gjIuucLqpuqmdIJYvtj69S8UaYDkvPM_I_fTIFaLtjd1tgZ9Uvj8jn2qP2FRavL6Sp4nTl7nxtfteKqLGieNOT_g1Ju3nWA2K7cKF40Z/s960/problem-of-the-week-cognitive-cardio-middle-school-math%20(22).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="problem of the week cognitive cardio math (middle school math moments)" border="0" data-original-height="960" data-original-width="960" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQof5GA3vQJKvDt8gvDl69rnw9A9KZf6_phSgbpU_bYwEnlEVWrqCuzMRo9norn34FL1gWIcWDCu8RSIiMHVf1gjIuucLqpuqmdIJYvtj69S8UaYDkvPM_I_fTIFaLtjd1tgZ9Uvj8jn2qP2FRavL6Sp4nTl7nxtfteKqLGieNOT_g1Ju3nWA2K7cKF40Z/w320-h320/problem-of-the-week-cognitive-cardio-middle-school-math%20(22).JPG" title="problem of the week cognitive cardio math (middle school math moments)" width="320" /></a></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td class="tr-caption"><a href="https://cognitivecardiomath.com/free-resource-center/">Click to access</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"></div><div><br />
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To access all of the Problem of the Weeks, click <a href="https://cognitivecardiomath.com/free-resource-center/">here</a>!<br />
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<br /><br /></div>Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-67784871637074445382016-01-24T09:07:00.000-05:002016-01-24T09:07:25.820-05:00What's Math Got To Do With It? - Chapter 4<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPINpQdbkhsM3YQJhlTfuHUg9EBjHwghNtBp9TGbx1zxsqtTwhcDSHLnygHcnFtXOz-1nWuIJ8Y2K2ymAhi4B_RlLtEA6l6oC4JfrRaMVA1rc1ad7WMxyA82se_zE9XRKHhRJXttUaj7KN/s1600/mult+choic+tests.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPINpQdbkhsM3YQJhlTfuHUg9EBjHwghNtBp9TGbx1zxsqtTwhcDSHLnygHcnFtXOz-1nWuIJ8Y2K2ymAhi4B_RlLtEA6l6oC4JfrRaMVA1rc1ad7WMxyA82se_zE9XRKHhRJXttUaj7KN/s320/mult+choic+tests.png" width="320" /></a></div>
<b>Chapter 4: Taming the Monster</b><br />
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I definitely enjoyed chapter 4. The chapter discusses one of our favorite topics - testing.<br />
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A few statements that Boaler makes in the chapter are:<br />
* American children are tested more than ever and more than students in the rest of the world.<br />
* The tests used in the U.S. are rejected by most other countries.<br />
* Tests are damaging to schools, teachers, and students - to their health, hearts, and minds.<br />
* It's hard to find any multiple choice questions used in Europe or in any national assessment, in any subject, at any level. (I've always taken multiple choice tests - I had no idea they are not used everywhere! Anyone from a different country reading this - what are your tests like??) (Anyone in U.S. - are your tests mostly multiple choice?)<br />
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Boaler identifies reasons <b>not</b> to use multiple choice tests:<br />
1) Multiple choice testing is known to be biased.<br />
2) Timed multiple choice tests cause anxiety.<br />
3) The best thing a multiple choice test shows is the ability to complete a multiple choice test.<br />
4) Using questions that are <b>not </b>multiple choice allows teachers
to better assess student understanding, which includes the thinking that
the student does and expresses in words, numbers, and symbols. If students are
simply choosing a correct answer, this information won't be available. <br />
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According to Boaler, tests in most states are extremely narrow - they don't assess thinking, or problem solving. Instead, they assess the use of procedures. She states that in the U.S., math teachers must focus on teaching what will be <i>tested</i>, rather than on what students need to know <i>for work or for life</i>. What about you? Do you agree with this statement in regards to your school/class?<br />
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Boaler states that with the Common Core era, free-response items will replace some multiple-choice items (on the state tests my students take, we've had multiple choice with several free-response for quite a long time now-before Common Core).<br />
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The results of standardized tests label students as low achievers, or "below average," and help to create low-achieving students; the label destroys their confidence and gives them the identity of a low-achiever. Research reveals that confidence in one's ability to succeed in math in an intrinsic part of success and motivation.<br />
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Boaler identifies "assessment <i>for</i> learning" as an alternative to the traditional "assessment <i>of </i>learning." This is a form of assessment that gives useful information to teachers and parents, but also allows students to take charge of their own learning. Assessment for learning is based on the idea that students should have:<br />
1) A clear sense of exactly what they are learning (the concept - not the page number or chapter title):<br />
Students have math goals to work toward - details about important concepts and how they are linked. These should be clear statements that express what students should be understanding. The example Boaler gives is, "I have understood the difference between mean and median and know when each should be used." Boaler cites an interesting study that showed great gains in low-achieving students whose class used this approach; it concluded that the students had previously been unsuccessful not because of a lack of ability, but because they hadn't known what they were supposed to be focused on.<br />
2) Where they are in the achievement of mastery. Students can show their self-assessment by putting red, yellow, or green stickers on their work; teachers can use red, yellow, or green cups for students to display. Boaler does note that students in research studies were hesitant to show red to begin with. However, after "green cup" students were asked to explain their understanding, students who didn't understand became more willing to show red.<br />
3) What they need to do to be successful. Teachers need to give constructive feedback about student work, rather than just giving a score. Boaler shares research that indicates that giving a grade can actually <i>reduce</i> achievement because the focus becomes the grade rather than what needs to happen for the student to improve. (Grades are fine at the end of the semester or term, she says). She relates this to coaching athletes - athletes aren't given grades; they are given advice and coaching to become better.<br />
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"Assessment for learning transforms students from passive receivers of knowledge to active learners who regulate their own progress and knowledge and propel themselves to higher levels of understanding."<br />
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It's 2016. That blows my mind. So many new ideas to think about, so many new things to try, so many hopes for the year! I hope the year will be good for you all!<br />
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This week's problem requires students to search for how many different combinations are possible for a password....can be challenging, depending on your students' background!<br />
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I hope you'll give it a try - if you do, please let me know how it goes! We have spent many days this school year giving our students the opportunity to "struggle" a bit with problems like these, and this had lead to great discussion, among the students AND the teachers.<br />
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Have a great Monday!<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhokP6gQkNo_DVVGPbEWTnBuUzYksbBWyso84nk0OHkQnWyUtkhazE6K4J_cf5IPwSoY_sWd0Mm7yBkRov-sudGW928AZ4fbg8sQUfJbDGKKlD5Jgwyavmao651jhVNTDcJa2Yig22B7OMna9MPCKVgNqG76_5Bp2NbjJvo1Xb7P5r-KHb7_5ixM9zFtDuf/s960/problem-of-the-week-cognitive-cardio-middle-school-math%20(21).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="problem of the week cognitive cardio math (middle school math moments)" border="0" data-original-height="960" data-original-width="960" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhokP6gQkNo_DVVGPbEWTnBuUzYksbBWyso84nk0OHkQnWyUtkhazE6K4J_cf5IPwSoY_sWd0Mm7yBkRov-sudGW928AZ4fbg8sQUfJbDGKKlD5Jgwyavmao651jhVNTDcJa2Yig22B7OMna9MPCKVgNqG76_5Bp2NbjJvo1Xb7P5r-KHb7_5ixM9zFtDuf/w200-h200/problem-of-the-week-cognitive-cardio-middle-school-math%20(21).JPG" title="problem of the week cognitive cardio math (middle school math moments)" width="200" /></a></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td class="tr-caption"><a href="https://cognitivecardiomath.com/free-resource-center/">Click to access</a></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;">To access all of the Problem of the Weeks, click </span><a href="https://cognitivecardiomath.com/free-resource-center/" style="text-align: left;">here</a><span style="text-align: left;">!</span></div>Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-22477320448285222082015-12-28T07:45:00.002-05:002016-01-24T09:07:17.459-05:00What's Math Got to Do with It? - Chapter 3Chapter 3: A Vision for a Better Future, <i>Effective Classroom Approaches</i><br />
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In Chapter 3, Boaler describes two successful approaches that offered students experiences with real math work. These approaches were used in studies that Boaler conducted. The study details that she shares are very interesting (I love reading about research), and I've included the highlights here.<br />
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Boaler calls the first approach the Communicative Approach. She completed a four-year study, following about 700 students in three different high schools, to determine that this is a successful approach. Students at one particular school were detracked, algebra became the first course that <i>all </i>students took when entering high school, and the teachers met over several summers to design/alter their courses. In this approach the focus is on "multiple representations," like words, diagrams, tables, symbols, objects, and graphs. The students at this school explained their work to each other, and moved between different representations and communicative forms. Interestingly, these students defined math as a form of communication, or a language. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXoXdv-SeT1xOrcS2avuYcdsiZPCcykYrzbhLRFLsvrR9aRQtN09bYUmWv8g6Hi5Wgu6Mw1oFNqdtEf12yGqeRx0zV72MXX36qJJhxycnRZCuyBXPoraV2UfwXKPETeE_wNI9_F0tNYrLV/s1600/good+at+math.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXoXdv-SeT1xOrcS2avuYcdsiZPCcykYrzbhLRFLsvrR9aRQtN09bYUmWv8g6Hi5Wgu6Mw1oFNqdtEf12yGqeRx0zV72MXX36qJJhxycnRZCuyBXPoraV2UfwXKPETeE_wNI9_F0tNYrLV/s320/good+at+math.png" width="320" /></a>The students taught with this approach worked in groups and were taught that they
are all smart, but have different strengths in different areas;
everyone had something important to offer. The teachers involved in this approach reinforced the idea that being good at math involves asking questions, drawing pictures and graphs, rephrasing problems, justifying methods, and representing ideas, in addition to calculating. They also followed an instructional design (called complex instruction) that made group work more effective and promoted equity among the students. Students at this school learned to appreciate the differences in one another.<br />
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In comparison to the students in the other, more suburban high schools in the study (using traditional teacher-lecture methods), the students at this urban school ended up outperforming the others on algebra and geometry tests by the end of the second year of high school. By their senior year, 41% of the students in the urban district were taking precalculus and calculus, compared to 23% at the other schools.<br />
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<a href="http://www.amazon.com/gp/product/0143128299/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0143128299&linkCode=as2&tag=midschmatmoma-20&linkId=NI5MBUBF67YJZIF2" rel="nofollow" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&ASIN=0143128299&Format=_SL250_&ID=AsinImage&MarketPlace=US&ServiceVersion=20070822&WS=1&tag=midschmatmoma-20" height="320" width="211" /></a>The other approach Boaler describes is the Project-Based Approach. Students in two schools were followed for three years in this study, which included the observation of hundreds of hours of lessons, interviews with and surveys of students, as well as various assessments. As the name indicates, students in this group worked on projects that addressed math as a "whole" rather than as separate areas of math. In many cases, students were taught certain methods when they needed to use them in the course of a project, rather than being taught the concepts beforehand. For example, in a particular area-related project, some students ended up needing to use trig ratios, so the teacher taught them about trig ratios.<br />
The projects were open enough that students could go in different mathematical directions - directions that interested them. Students could choose who to work with, so some worked alone, some in pairs, and some in groups.<br />
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The students at this school viewed mathematical methods as "flexible problem-solving tools," and ended up scoring higher than the national average on their exams, taken at age 16. For more details, you may want to read the book Boaler has published about this study -<i> Experiencing School Mathematics</i>.<br />
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As a result of her studies, Boaler concludes that students need to be actively involved in their learning and they need to be engaged in a broad form of math.<br />
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Do any readers use a project-based approach to teach math? If so, how does it work for you?<br />
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Ehttp://www.blogger.com/profile/15364109438884379886noreply@blogger.com0tag:blogger.com,1999:blog-1865532893643812161.post-80865955689970831782015-12-06T22:21:00.003-05:002024-01-19T11:16:24.216-05:00Problem of the Week, #8<div style="text-align: center;">
All problems are now on my new site: <a href="https://cognitivecardiomath.com/free-resource-center/">https://cognitivecardiomath.com/free-resource-center/</a></div>
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This week's problem can be solved by guessing and checking or by setting up an equation and solving algebraically, so no matter where your students "are," they can give it a shot:-)<div><br /></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0TDaItKBnNUwr74te4FH7BZMO-OxwSO1_7uIBW91jrCtrKF5pY43jJpW1T6XwJqzcwAcI_eJ2Wfg46XoxKgB7N2e04iPHXh1iuDRVDRyjQdrqtfpxHxS0xnMstqVFFLhB_Ns6IkYUgRlg3ySjJyo_RaFHHLLn6uzo4I0wVyqpCmlYlMuJ2moh8JOlDY9Q/s960/problem-of-the-week-cognitive-cardio-middle-school-math%20(20).JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="problem of the week cognitive cardio math (middle school math moments)" border="0" data-original-height="960" data-original-width="960" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0TDaItKBnNUwr74te4FH7BZMO-OxwSO1_7uIBW91jrCtrKF5pY43jJpW1T6XwJqzcwAcI_eJ2Wfg46XoxKgB7N2e04iPHXh1iuDRVDRyjQdrqtfpxHxS0xnMstqVFFLhB_Ns6IkYUgRlg3ySjJyo_RaFHHLLn6uzo4I0wVyqpCmlYlMuJ2moh8JOlDY9Q/w200-h200/problem-of-the-week-cognitive-cardio-middle-school-math%20(20).JPG" title="problem of the week cognitive cardio math (middle school math moments)" width="200" /></a></div><br /><div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td class="tr-caption"><a href="https://cognitivecardiomath.com/free-resource-center/">Click to access</a></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"></div><br /> To access all of the Problem of the Weeks, click <a href="https://cognitivecardiomath.com/free-resource-center/">here</a>!<br />
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