tag:blogger.com,1999:blog-68754957172431679332024-02-26T19:11:10.301-05:00A Little StatsAdventures in Teaching StatisticsAmy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.comBlogger40125tag:blogger.com,1999:blog-6875495717243167933.post-43829927979998523382021-06-12T08:59:00.000-04:002021-06-12T08:59:05.415-04:00ASA Podcast: Practical Significance<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiWYr9IJ3YnH4OsB6M6M0ORp4OtJqrKSRePR2kXVh7nicLkmVT_-9NeV9Da34mGuXkseOA1r80Kj9pyz85i2L5p63Y8YJX2soNXL0yT6i-OTHwra9gyiBYDydg7FwzL3GhHwCfflIrRJzq/s1400/practical-significance.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1400" data-original-width="1400" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiWYr9IJ3YnH4OsB6M6M0ORp4OtJqrKSRePR2kXVh7nicLkmVT_-9NeV9Da34mGuXkseOA1r80Kj9pyz85i2L5p63Y8YJX2soNXL0yT6i-OTHwra9gyiBYDydg7FwzL3GhHwCfflIrRJzq/s320/practical-significance.jpg"></a></div>Have you been listening to the new-ish ASA podcast? Hosted by Executive Director Ron Wasserstein and Director of Strategic Initiatives and Outreach Donna LaLonde, it's a nice way to spend a subway morning commute. Bonus: I was recently invited to join in on the conversation!<p></p><span></span><a href="https://alittlestats.blogspot.com/2021/06/asa-podcast-practical-significance.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-77094837695367351892021-01-02T18:19:00.005-05:002021-01-02T18:19:54.849-05:0051 Ideas for Stress Relief... from my AP Statistics Students<div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJMR-XcSJiDBk_hgSYHFL_VW3IjDyV6JeB62CH_YJJgAPh_LGdrrw12c-7iQOk4j3xx4M2dwCAd-kJW2r4OyFMwtIDWdTxuRUN2qzryi4C8JHBD7ZCD0YK0tvUzBQNk-qT4NHbvax-6rYm/s1378/stressrelief.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="780" data-original-width="1378" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJMR-XcSJiDBk_hgSYHFL_VW3IjDyV6JeB62CH_YJJgAPh_LGdrrw12c-7iQOk4j3xx4M2dwCAd-kJW2r4OyFMwtIDWdTxuRUN2qzryi4C8JHBD7ZCD0YK0tvUzBQNk-qT4NHbvax-6rYm/s320/stressrelief.png" width="320"></a></div></div><div>I asked my students: "What are you currently doing for stress relief?" </div><div><br></div><div>Most had really great, healthy things they are doing. I love how some of my students were vague about what they are doing and some were very specific. One wise student started by saying, "I've been trying to tell myself that I'm doing my best and I'm only human." But some said, "Nothing. I am very stressed." Or, "I'm really just upset a lot." And one student used this space to say: "I'm currently struggling to find a way. I would love to hear our classmate's responses." </div><div><br></div><div>And so, I decided to compile a list of my students' responses.<span></span></div><a href="https://alittlestats.blogspot.com/2021/01/stressrelief.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-91963216910307790692020-12-13T09:52:00.003-05:002020-12-14T12:35:27.465-05:00Top 6 Strategies for Building a Successful Remote Classroom<p class="XzvDs _208Ie ljrnk blog-post-text-font blog-post-text-color _2QAo- _25MYV _1Fao9 ljrnk public-DraftStyleDefault-block-depth0 public-DraftStyleDefault-text-ltr" id="viewer-741fj" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; direction: ltr !important; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: 1.38; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span class="vkIF2 public-DraftStyleDefault-ltr" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; color: var(--ricos-custom-p-color,unset); direction: ltr; display: block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_PP0rzl2I1CvlNWDzJPSm6i87k5r3ASa_qDosuI7CAOQh2GNy6aKAz9wTdrgbiMnGd3c6uNm0bSBSryjOsTnjLUQQuz1poc1SA2_QDH6ZR27-UVaJQeGwzKw_H1P1MX3ZnRUy2a_I-PrX/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img data-original-height="1066" data-original-width="1628" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_PP0rzl2I1CvlNWDzJPSm6i87k5r3ASa_qDosuI7CAOQh2GNy6aKAz9wTdrgbiMnGd3c6uNm0bSBSryjOsTnjLUQQuz1poc1SA2_QDH6ZR27-UVaJQeGwzKw_H1P1MX3ZnRUy2a_I-PrX/w320-h210/image.png" width="320"></a></div><div style="text-align: left;"><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">When Luke Wilcox </span><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">asked me how this semester was going </span><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">and to write a blog post for </span><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><i>Stats Medic</i></span><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">, I had to tell him the truth. I told him about the rollercoaster semester we've (all) had so far. I also didn't hesitate at the chance to write the requested post. In part because it felt good to get reacquainted with my blog-writing self, but also because </span><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><i>Stats Medic</i></span><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"> generously enrolled all of my students last semester to their online AP Statistics course free of charge just weeks after we went into emergency remote learning. New York City was hit pretty hard by this pandemic early on and I was very grateful to have this resource for my students. My generous statistics community has helped me immensely throughout this challenging year and I knew this would be a way for me to help pay it forward. </span></div></span></div><span class="vkIF2 public-DraftStyleDefault-ltr" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; color: var(--ricos-custom-p-color,unset); direction: ltr; display: block; font-family: inherit; font-size: inherit; font-stretch: inherit; font-variant: inherit; font-weight: inherit; line-height: inherit; margin: 0px; outline: 0px; padding: 0px; text-align: left; vertical-align: baseline;"><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><br></span></span><span class="vkIF2 public-DraftStyleDefault-ltr" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; direction: ltr; display: block; font-stretch: inherit; font-variant-east-asian: inherit; font-variant-numeric: inherit; line-height: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;"><span style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0); background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; box-sizing: inherit; color: var(--ricos-custom-p-color,unset); font: inherit; margin: 0px; outline: 0px; padding: 0px; vertical-align: baseline;">Luke asked </span>"If you have one thing to share with the AP Stats community, what would be most helpful?" After thinking about this good question, I had more than one thing. This post is my response.</span><span></span><p></p><a href="https://alittlestats.blogspot.com/2020/12/top-6-strategies-for-building.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-52672765093717668532018-08-22T08:00:00.000-04:002019-08-07T11:57:43.773-04:00Student Questionnaire<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6NseWZFCKIafOGD5FKWiOHaWdayKq-XWYbzDMe1cYyI_4RkOF7drlt_slB6orfzEnjFMh4qUbVKOgf5CW-OwoU7I9FrdTyhu9vCaDY0zY_AUf5q5mEgCeZXEdNUmJYMM9wa4aja9nVDsc/s1600/toiletpaperorientation.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1143" data-original-width="1600" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6NseWZFCKIafOGD5FKWiOHaWdayKq-XWYbzDMe1cYyI_4RkOF7drlt_slB6orfzEnjFMh4qUbVKOgf5CW-OwoU7I9FrdTyhu9vCaDY0zY_AUf5q5mEgCeZXEdNUmJYMM9wa4aja9nVDsc/s400/toiletpaperorientation.jpg" width="400"></a></div>
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Do you give your students a questionnaire at the beginning of the school year? I've been giving one every year since I started teaching but it changes from year to year. Some questions I ask to gather information I need about my students, some are to get to know my students a little bit, and some are just for fun. The past couple of years, some of the questions I ask are to gather data that I then use in aggregate in my AP Statistics class activities.<br>
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Here are some of the things I've been asking my students...<br>
<a href="https://alittlestats.blogspot.com/2018/08/student-questionnaire.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-17394508708134621082018-07-21T08:00:00.000-04:002018-07-21T15:45:01.995-04:00Building Support Communities for Statistics Educators<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXY4hn6m71RcgFmA6VzChK4SDK-iZmZud6xlttEvXfWfKRN5vzwUPAu_2xbq_JJEWXlChbuhXiCjkDv744h3aL9MOJ9BShzryRJbNLEhWIIfCM7q6sGMLBifsT2YOgRPPwJ-vkItmkIfr7/s1600/kyoto.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1145" data-original-width="1600" height="454" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXY4hn6m71RcgFmA6VzChK4SDK-iZmZud6xlttEvXfWfKRN5vzwUPAu_2xbq_JJEWXlChbuhXiCjkDv744h3aL9MOJ9BShzryRJbNLEhWIIfCM7q6sGMLBifsT2YOgRPPwJ-vkItmkIfr7/s640/kyoto.JPG" width="640"></a></div>
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It's been a week since I returned home from Japan and I think I am finally recovered from the jet lag. At least, I hope I am. I spent a couple of days in Tokyo, then took the Shinkansen to Kyoto for the 10th International Conference on Teaching Statistics (ICOTS). Lynette Hudiburgh [of Miami University] and I presented about a topic near and dear to us – statistics teacher support communities.<br>
<a href="https://alittlestats.blogspot.com/2018/07/building-support-communities-for.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-45545831706372344212018-06-23T09:00:00.000-04:002020-02-26T18:03:19.304-05:00Fake Data<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiY9FC1KO65uNYIttIltLu6UTTDRP5Nx8FLwRYoibTPWk9Q41oROa6gMd8xmdT25TBJOcHQgb6muE0PNO-RT7eP5vBFJggV5_xEq_UoGDrQoezJUG7aI_v3SQ2Ewwp7A6Xe8JD9wQEIoQNo/s1600/FakeData1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="540" data-original-width="720" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiY9FC1KO65uNYIttIltLu6UTTDRP5Nx8FLwRYoibTPWk9Q41oROa6gMd8xmdT25TBJOcHQgb6muE0PNO-RT7eP5vBFJggV5_xEq_UoGDrQoezJUG7aI_v3SQ2Ewwp7A6Xe8JD9wQEIoQNo/s640/FakeData1.jpg" width="640"></a></div>
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This year my math department focused on student engagement in our professional development meetings. My AP Statistics colleagues (Doug Shuman and Alexandra Brennan) and I developed this activity for the 𝜒² unit as a result and the three of us implemented it in our classrooms. Here's a little information about this two-part activity. Even though our students faked their data, it was a real success!<br>
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<a href="https://alittlestats.blogspot.com/2018/06/fake-data.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-71295686776465535062018-05-14T16:42:00.002-04:002018-05-14T16:42:18.292-04:00The Final AP Stats Power Quiz<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibI_PifFiTMHKQgZJlHl6lH1dOB_DL3pRfEpnl2jODvOw4f5pHy4J0rE2JtoecMWlva6fjezOTjA8F1JHCy-ranzfEoHQlD3oRRXIt6IJEjs_chOWbiT_Xh3zxBldC1vv_Ge9i7xPDOgMG/s1600/powerquiz.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="562" data-original-width="562" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibI_PifFiTMHKQgZJlHl6lH1dOB_DL3pRfEpnl2jODvOw4f5pHy4J0rE2JtoecMWlva6fjezOTjA8F1JHCy-ranzfEoHQlD3oRRXIt6IJEjs_chOWbiT_Xh3zxBldC1vv_Ge9i7xPDOgMG/s320/powerquiz.jpg" width="320"></a>As a way to review for the AP Stats exam, I have my students do a series of power quizzes* (5 multiple choice questions) in the weeks leading up the exam date (either individually or in groups). This is common practice in my department. A colleague of mine also does a final power quiz the day before the AP exam. I loved the idea so much that I decided to use this inspiration to come up with my own final power quiz for my AP Stats students.<br>
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<a href="https://alittlestats.blogspot.com/2018/05/the-final-ap-stats-power-quiz.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-55822770309841426132017-08-28T10:00:00.000-04:002018-08-22T13:18:04.968-04:00Common Core Algebra II: Students' Heights<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJCQEKEhN4QIwldMdITuuB9yR90cF0m8z2rDXCZxXaiobuNpFJyI14lctdkAzSCjAP9PxeaqN0nPYpW4a46trWgAuwxSyElJW5om0R0lb3uUWZzUazfJbqiBZWsiPhTsjIQKmKG6isMq2X/s1600/CCAIIJun2017_15.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="300" data-original-width="648" height="296" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJCQEKEhN4QIwldMdITuuB9yR90cF0m8z2rDXCZxXaiobuNpFJyI14lctdkAzSCjAP9PxeaqN0nPYpW4a46trWgAuwxSyElJW5om0R0lb3uUWZzUazfJbqiBZWsiPhTsjIQKmKG6isMq2X/s640/CCAIIJun2017_15.jpg" width="640"></a></div>
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Patrick Honner does a wonderful Regents recap over on his blog. In today's post, he discusses this statistics question from the June 2017 NYS Algebra II Regents exam. I started this as a comment on his post, but it of course got a little too out of hand for a comment.<br>
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So here is my response. These are the many things I dislike about question 15 and how I would make it better.<br>
<a href="https://alittlestats.blogspot.com/2017/08/common-core-algebra-ii-students-heights.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com3tag:blogger.com,1999:blog-6875495717243167933.post-67174207135420024352017-05-29T08:00:00.000-04:002017-05-29T12:04:26.182-04:00Video: Random Sampling<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPFHx2SU0tR598amtCc60B5VulCkb9hLE4B-kbOPyLLf0U2xIExz-vFsf0NqOGxpJmR5nfp1wXlbr96axMcuKT9Fbsjac2piDFo7WCTt94VlaMCNq0xRXFUd-hA76F88rW6jjxnCWEaTJG/s1600/randomsampling.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="314" data-original-width="600" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPFHx2SU0tR598amtCc60B5VulCkb9hLE4B-kbOPyLLf0U2xIExz-vFsf0NqOGxpJmR5nfp1wXlbr96axMcuKT9Fbsjac2piDFo7WCTt94VlaMCNq0xRXFUd-hA76F88rW6jjxnCWEaTJG/s1600/randomsampling.jpeg"></a></div>
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Pew Research Center has just launched <i>Methods 101</i>, "a new occasional video series dedicated to explaining and educating the public about the basic methods we use to conduct our survey research."<br>
<a href="https://alittlestats.blogspot.com/2017/05/video-random-sampling.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-22859643641905592232017-03-04T08:00:00.000-05:002017-03-04T11:54:42.887-05:00Statistical Distributions<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ1Mt-cHKl09shhRPesirNNQPurintDZTvjjysKiH3FXg7qgpUgzT3xfzzP8BdWj5BCIjUDDOiCtx3YYypSXaJCpior1zTi4QGyOsESiEdTUtOt5owwrQImUnhyphenhyphenpScat9snTHTs0j3ujpp/s1600/distributions2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="264" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ1Mt-cHKl09shhRPesirNNQPurintDZTvjjysKiH3FXg7qgpUgzT3xfzzP8BdWj5BCIjUDDOiCtx3YYypSXaJCpior1zTi4QGyOsESiEdTUtOt5owwrQImUnhyphenhyphenpScat9snTHTs0j3ujpp/s640/distributions2.JPG" width="640"></a></div>
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Which one doesn't belong?<br>
<a href="https://alittlestats.blogspot.com/2017/03/statistical-distributions.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com2tag:blogger.com,1999:blog-6875495717243167933.post-35195351502286891702017-02-18T08:00:00.000-05:002017-02-18T13:14:13.666-05:00Total Amount of Skittles: Fixed or Variable?<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixFwveRzg9mRI7ai0QHwUkHt_h7I2QRIjn7WANJpVu0H6oCDXHDm1GwjAWgzOBXdXgaI7RHkXewl-wshcewlrio7aWHcqWNwk_vCV5aFb13QicjuuVUpWwRiISujMicyHuWVfpirjSGpyk/s1600/SkittlesFunsize.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/AVvXsEixFwveRzg9mRI7ai0QHwUkHt_h7I2QRIjn7WANJpVu0H6oCDXHDm1GwjAWgzOBXdXgaI7RHkXewl-wshcewlrio7aWHcqWNwk_vCV5aFb13QicjuuVUpWwRiISujMicyHuWVfpirjSGpyk/s320/SkittlesFunsize.jpg" width="320"></a></div>
Today, I read a great post from Dan Meyer talking about a 3-Act lesson he did in an elementary school having students estimate the total number of Skittles in a jar. A statement he made got me thinking about the variability or fixed nature of the total.<br>
<a href="https://alittlestats.blogspot.com/2017/02/total-amount-of-skittles-fixed-or.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com2tag:blogger.com,1999:blog-6875495717243167933.post-41626552327667690052017-02-10T08:00:00.000-05:002017-02-12T12:56:49.116-05:00Common Core Algebra II: A Truckload of Oranges?<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCgKNYBu1yacZvjTwqSIU3AgMI1rN3vcBoSzSWEuIM70VE4LrAK6-2SSZPcHF3ynJsKkTxsJLgGT45rdHRAeXHwgaS7kusbhMdpURbUBa2R0s4gh32xSi4qc0rUNeyuUjehiqUr9MV0opF/s1600/Oranges.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCgKNYBu1yacZvjTwqSIU3AgMI1rN3vcBoSzSWEuIM70VE4LrAK6-2SSZPcHF3ynJsKkTxsJLgGT45rdHRAeXHwgaS7kusbhMdpURbUBa2R0s4gh32xSi4qc0rUNeyuUjehiqUr9MV0opF/s320/Oranges.JPG" width="320"></a></div>
Can someone please explain to me WTH "The Orange" question (#26) from the January 2017 Common Core Algebra II Regents was asking?<br>
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This question is... just, wow. Where do I even begin?<br>
<a href="https://alittlestats.blogspot.com/2017/02/a-truckload-of-oranges.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com2tag:blogger.com,1999:blog-6875495717243167933.post-87972864162698863102017-01-20T08:50:00.005-05:002017-01-20T08:50:54.343-05:00Keep Calm...<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMuoXBt7A-fGaw1ay18NeqeMn74JJkRId9MX6LaBGYoAPSa25_0qJhg55ef67GxBzHYNQTsUmRelJ9LFRgQh6_C2_6RZLrndaIi-cSDc3WpwulU6dlIqSxlXgzgWFxqz6DVNhEzk_WKBjH/s1600/keepcalmandlearnstats.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMuoXBt7A-fGaw1ay18NeqeMn74JJkRId9MX6LaBGYoAPSa25_0qJhg55ef67GxBzHYNQTsUmRelJ9LFRgQh6_C2_6RZLrndaIi-cSDc3WpwulU6dlIqSxlXgzgWFxqz6DVNhEzk_WKBjH/s1600/keepcalmandlearnstats.jpg" /></a></div>
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Now more than ever...</div>
<br />Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-78634446192731570172016-12-02T06:00:00.000-05:002016-12-02T06:00:26.677-05:00MfA Fall Function: Why I Stay<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOaTML6t7BjdRn_1Adnfg0rOMLagiggrQXThe7eIBW3gH-82GBSutjW3run0pVnL-dQ3kRHOLvyzyuBMHhKTSO2Uu9dhf48RqvflD3638tIRbaSPfJuRWbnFr74KfYoDGbWdNBoxFy-x5U/s1600/AmyMfAFallFuntion2016-001.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="319" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOaTML6t7BjdRn_1Adnfg0rOMLagiggrQXThe7eIBW3gH-82GBSutjW3run0pVnL-dQ3kRHOLvyzyuBMHhKTSO2Uu9dhf48RqvflD3638tIRbaSPfJuRWbnFr74KfYoDGbWdNBoxFy-x5U/s320/AmyMfAFallFuntion2016-001.jpg" width="320"></a></div>
A few weeks ago, I had the honor of being asked to be the teacher keynote speaker at the 10th Annual MƒA Fall Function. Early in writing my speech it became clear that my speech should be about me, about the positive impact MƒA has had on my teaching career, but most importantly about what I feel makes MƒA so meaningful to someone like me.<br>
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The following is the speech I gave:<br>
<a href="https://alittlestats.blogspot.com/2016/12/mfa-fall-function-why-i-stay.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com2tag:blogger.com,1999:blog-6875495717243167933.post-8217804995273512282016-11-02T06:00:00.000-04:002016-11-02T07:39:17.916-04:00Thanks to the... Election, Statistics is Cool Again<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdCj5cMJAAJeEvprIewSWVTlmFdtPm1PbD1uQwtzNQ0vZyIV498twRuFpuljLT5gvfHckOVluVb72N_QNskJHnvvD0pvcCU5DGs2PtJ2XtILogtz7rCfM4YTYDQsaIGPqKoPEWZS3y0o5E/s1600/MT2election.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="317" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdCj5cMJAAJeEvprIewSWVTlmFdtPm1PbD1uQwtzNQ0vZyIV498twRuFpuljLT5gvfHckOVluVb72N_QNskJHnvvD0pvcCU5DGs2PtJ2XtILogtz7rCfM4YTYDQsaIGPqKoPEWZS3y0o5E/s640/MT2election.png" width="640"></a></div>
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Way back in 2012, Ellie Terry Vierling and I presented "Thanks to the 2012 Election, Statistics is Cool Again" at the inaugural MƒA MT<sup>2</sup>: Master Teachers on Teaching. Ellie and I looked at statistically modeling issues related to the election and cowrote an activity that we conducted in our classrooms. Guess what? Despite the fact that the 2016 presidential election is just slightly more bananas, it's still relevant.<br>
<a href="https://alittlestats.blogspot.com/2016/11/thanks-to-election-statistics-is-cool.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-30236861051180362132016-10-24T06:00:00.000-04:002016-10-25T09:04:08.046-04:00Teaching Ideas to Prepare Your Students for the AP Stats Exam<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5Tm2HKUBORG4k3mOYBDRB0dNyHBSVwsISLEHMq62m__CSEfdCCr_FGS8h-xZVOQDInv6DfbYi1pMzYRCVT-rDn28Oaycdwa23oWMjlhf85k_XRdvA8dOz9vf2nShOwZF5FvrTbavdPRef/s1600/APStatsGlobalMathDept.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5Tm2HKUBORG4k3mOYBDRB0dNyHBSVwsISLEHMq62m__CSEfdCCr_FGS8h-xZVOQDInv6DfbYi1pMzYRCVT-rDn28Oaycdwa23oWMjlhf85k_XRdvA8dOz9vf2nShOwZF5FvrTbavdPRef/s640/APStatsGlobalMathDept.jpg" width="640"></a></div>
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Did you miss the Global Math Department webinar Bob Lochel, Doug Tyson, and I did a couple of weeks ago? Fear not, you can watch the archived video.<br>
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<a href="https://alittlestats.blogspot.com/2016/10/teaching-ideas-to-prepare-your-students.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-3720556158334114792016-09-24T08:00:00.000-04:002016-09-24T08:46:58.402-04:00The Joy of Stats<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh37Q9gSJ2CUdhzvXjo_XR3cY6DjojqpkcbVc68Oa8jcFndT21xgK1_n2g16cxLcEvO2TqxkyP1cTd-Kt-HUjE5NZS5GNHXYO-17TdaM7LaqsubY5rHAfJWksOM4NFx5HJdMHtiuxcqSh4O/s1600/joyofstats.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="225" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh37Q9gSJ2CUdhzvXjo_XR3cY6DjojqpkcbVc68Oa8jcFndT21xgK1_n2g16cxLcEvO2TqxkyP1cTd-Kt-HUjE5NZS5GNHXYO-17TdaM7LaqsubY5rHAfJWksOM4NFx5HJdMHtiuxcqSh4O/s400/joyofstats.jpg" width="400"></a></div>
Hans Rosling has a bit of a cult following. In 2010, he aired an hour-long program on BBC, <i>The Joy of Stats</i>, and it has been one of my favorite statistics videos.<br>
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<a href="https://alittlestats.blogspot.com/2016/09/the-joy-of-stats.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-24550893534293490862016-09-15T06:00:00.000-04:002016-09-15T06:16:09.807-04:00U.S. Census Bureau: Statistics in Schools<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi02OCs28H1b9acujAnfpuU0vM5LeIJg7eXUTLdVgq_FDRebhsbSFHJpvrt3wuJslqYikE86DnPWI0yH67Ipd0g6CX-d8-_WcMokEzP36caW8HnfOuMuPiOB6iGyEiGhvpv1ddrkLAR0Tfe/s1600/statisticsinschools.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi02OCs28H1b9acujAnfpuU0vM5LeIJg7eXUTLdVgq_FDRebhsbSFHJpvrt3wuJslqYikE86DnPWI0yH67Ipd0g6CX-d8-_WcMokEzP36caW8HnfOuMuPiOB6iGyEiGhvpv1ddrkLAR0Tfe/s1600/statisticsinschools.jpg"></a></div>
The U.S. Census Bureau unveiled its newly updated <i>Statistics in Schools</i> program for K-12 teachers and students earlier this month. Using current and historical data, the Census Bureau program provides teachers the tools to help students understand statistical concepts and improve their data analysis skills. There are free online activities and other resources available in geography, history, social studies, sociology, as well as math.<br>
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It looks good.<br>
<a href="https://alittlestats.blogspot.com/2016/09/us-census-bureau-statistics-in-schools.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-92204218227686276732016-09-08T06:00:00.003-04:002021-06-12T09:59:25.706-04:00Statistics Education & Social Justice<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieQyXVWhdwsqKdl4JKjamRJ-kkpJIhkohRKCg_kaoa2sDfhsTQBL-x9jkQfamZD8zADuj6ExAQTSe4LjeXEB6z9M6S9EN_nrv-Wyl1iQLmRHSQbGqO5tsB9CmcXFeb197FcLq9kFiWsEBc/s1600/statssocialjustice.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieQyXVWhdwsqKdl4JKjamRJ-kkpJIhkohRKCg_kaoa2sDfhsTQBL-x9jkQfamZD8zADuj6ExAQTSe4LjeXEB6z9M6S9EN_nrv-Wyl1iQLmRHSQbGqO5tsB9CmcXFeb197FcLq9kFiWsEBc/s1600/statssocialjustice.jpg"></a></div>
In August, I facilitated and attended a planning day with some fellow AP Statistics teachers at Math for America in NYC. We meet regularly throughout the year but we decided that the end of September was too long to wait to fully prepare for our year. Over a dozen of us showed up at the MƒA offices and spent over 4 hours discussing prep for our AP Stats courses. One of the main things on the agenda: how to incorporate social justice into our stats classes.<br>
<a href="https://alittlestats.blogspot.com/2016/09/statistics-education-social-justice.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com5tag:blogger.com,1999:blog-6875495717243167933.post-44831536057780787742016-09-02T08:00:00.000-04:002018-08-22T10:39:22.722-04:00TMC NYC 2016 and Commute Times<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGo17KbPz4Q1lJ-SRGKYHYm6DwPYsh2H8IsM-22-ryaX3nmq3TMN0JOap-cRLg_3g3U3W9zMrTsQ7Cf4mczrmNiWgJgVwZCo9yEVnqFyO3LFtxBdGK735n8QLfWv48luVK523iEEdEQ0on/s1600/IMG_5537.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: inherit;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGo17KbPz4Q1lJ-SRGKYHYm6DwPYsh2H8IsM-22-ryaX3nmq3TMN0JOap-cRLg_3g3U3W9zMrTsQ7Cf4mczrmNiWgJgVwZCo9yEVnqFyO3LFtxBdGK735n8QLfWv48luVK523iEEdEQ0on/s400/IMG_5537.JPG" width="300"></span></a></div>
<span style="font-family: inherit;">I had a really great time at the mini Twitter Math Camp (TMC) conference in NYC last month. I met up with a great group of teachers to discuss math and teaching. I also presented about the statistical investigation process using commute times as a context.</span><br>
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<a href="https://alittlestats.blogspot.com/2016/09/tmc-nyc-2016-and-commute-times.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-19898217655758874132016-08-17T07:00:00.000-04:002017-01-30T14:29:14.670-05:00Statistical Questions<div class="separator" style="clear: both; text-align: center;">
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What makes a question a statistical question? Furthermore, what makes a <u>good</u> statistical question?<br>
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The <a href="http://www.corestandards.org/Math/Content/6/SP/A/1/" target="_blank">Common Core State Standards (6.SP.A.1)</a> describes it like this:<br>
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... one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.</blockquote>
This statistics standard is slated for 6th grade students<sup><span style="font-size: xx-small;">1</span></sup>, but I recently heard a more effective explanation of what a statistical question is that will be relevant for middle school, high school, and college statistics. It also defines what makes a statistical question a good one, which the Common Core definition does not.<br>
<a href="https://alittlestats.blogspot.com/2016/08/statistical-questions.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-47542904219821894842016-08-11T08:00:00.000-04:002016-08-11T08:01:20.694-04:00ASA's Prediction 2016 Contest<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGgUnh4cOrxkF6d67l9tuoYeDm4QCkt1zJO1VE_ZgX5JNMGalA8zBvnxlrqZema_rCfokwX3msiVSzBnl8_jc1nzCmwioV6h9epYUgMOeDB2Gzj5-cgZUIy8klEWWAWEtkU45TfpQzoPgp/s1600/ASA_Prediction-2016_Banners_CP.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGgUnh4cOrxkF6d67l9tuoYeDm4QCkt1zJO1VE_ZgX5JNMGalA8zBvnxlrqZema_rCfokwX3msiVSzBnl8_jc1nzCmwioV6h9epYUgMOeDB2Gzj5-cgZUIy8klEWWAWEtkU45TfpQzoPgp/s640/ASA_Prediction-2016_Banners_CP.png" width="640"></a></div>
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The American Statistical Association has a challenge for stats-savvy students: predict* the next U.S. president!<br>
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Prediction* 2016 is a contest for high school and undergraduate college students to predict* the winner of the U.S. presidential election using statistical methods. Winners will receive a variety of prizes and perks, including exposure to the nation’s leading statisticians and data scientists.<br>
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<a href="https://alittlestats.blogspot.com/2016/08/asas-prediction-2016-contest.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com0tag:blogger.com,1999:blog-6875495717243167933.post-27537122864384811262016-05-20T08:00:00.000-04:002016-09-02T12:37:54.606-04:00Common Core Algebra II: Music and Gender<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht4M0sNrfejmLrbmAF4FAwyDcIWIxJll6aoxinok9F5bAuMfEjU4fcaJeEhNjSFGe_CztiuEev1U53xMC9CCJnZCoKnLPIxNMZyeYmDQBuaF62GrApTQylhoD_80CY4_TzkuUAAnjuPep-/s1600/F2015_08.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht4M0sNrfejmLrbmAF4FAwyDcIWIxJll6aoxinok9F5bAuMfEjU4fcaJeEhNjSFGe_CztiuEev1U53xMC9CCJnZCoKnLPIxNMZyeYmDQBuaF62GrApTQylhoD_80CY4_TzkuUAAnjuPep-/s640/F2015_08.jpg" width="640"></a></div>
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In Fall 2015, NYS released a set of sample questions for the new Common Core Algebra II Regents. They included this question regarding independence. I've done similar questions like this with my AP Statistics students. Here, I outline how I would improve and present this question to Algebra II students. In fact, I've created two enhanced versions of this problem.<br>
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<a href="https://alittlestats.blogspot.com/2016/05/common-core-algebra-ii-independence.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com6tag:blogger.com,1999:blog-6875495717243167933.post-67906812446034204952016-05-01T09:00:00.000-04:002016-09-08T08:27:43.403-04:00The Wrong Way to Target Math (Part III)<div class="separator" style="clear: both; text-align: center;">
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I have waited over two months to continue my thoughts on Andrew Hacker. To be honest, the draft of this post has been sitting untouched since my first two posts. I thought the wait might help me mollify my response to his <i>NY Times</i> OpEd pieces and <i>The Math Myth</i>. Largely, though, it hasn't. I am still just as frustrated as I was before. Here, I'll try my best to wrap up my thoughts because I am eager to put him out of my mind soon. My goal is to answer questions like "Who Needs Statistics?" and "Is Political Science Necessary?" But first, in order for you to fully understand, I'll need to talk about knitting. No, really.<br>
<a href="https://alittlestats.blogspot.com/2016/05/the-wrong-way-to-target-math-part-iii.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com2tag:blogger.com,1999:blog-6875495717243167933.post-50096169818396275472016-02-29T06:00:00.000-05:002016-05-01T21:28:18.728-04:00The Wrong Way to Target Math (Part II)<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfWTu-_u5V7r_w_6xG0J9eh9sx2YI9np1z3Gh1VeVYK2RCpBWwODRj_ffW6AxtSt6_hjAPIiOnjz8mwkFfM7DwdhBQaxQFJax5amJzKTHRPscAMZCSENtUETMFD57K4KF6vfw8uSRnAwgz/s1600/Hackergraph.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfWTu-_u5V7r_w_6xG0J9eh9sx2YI9np1z3Gh1VeVYK2RCpBWwODRj_ffW6AxtSt6_hjAPIiOnjz8mwkFfM7DwdhBQaxQFJax5amJzKTHRPscAMZCSENtUETMFD57K4KF6vfw8uSRnAwgz/s400/Hackergraph.jpg" width="358"></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Andrew Hacker: Which graph wore it better? </td></tr>
</tbody></table>
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Now that we've summarized the Hacker philosophy of math education, let's get back to my issues with the most recent Andrew Hacker OpEd regarding his insults to AP Statistics. This is where I start to get angry.<br>
<a href="https://alittlestats.blogspot.com/2016/02/the-wrong-way-to-target-math-part-ii.html#more">Read more »</a>Amy Hoganhttp://www.blogger.com/profile/16977577345624584601noreply@blogger.com10