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June 23, 2008

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I am delighted to report that last week this blog went over 100,000 page views since its inception. That is certainly a dream come true for me. Many thanks to everyone who has been kind enough over the years to mention this blog to all of the teachers around you. As a new year begins, please continue to let people in the education profession know that I try to post my thoughts on teaching 2 or 3 times each month. Thanks!!! ** About 10 days ago, I released my new book on Amazon: Don�t Just Dream about Success: Stack the Odds in Your Favor . As the title clearly implies, I believe that everyone can become more successful more of the time by following certain tactics. Proceeds from the sale of this book go to finance CPA review for FREE, the website ( www.CPAreviewforFREE.com ) where candidates can prepare to pass the CPA exam without having to spend a fortune. I sim...

CLOSING THE HOLES ON SWISS CHEESE KNOWLEDGE

January 23, 2018

Over the years, I have argued often on this blog that one of the really weak spots in education was the failure of students to close the holes on what I call �Swiss Cheese Knowledge.� Thus, on the first day of class last week, I drew a block on the board and put holes in it. I then explained the drawing to my students. When you leave class every day, your knowledge looks like a block of Swiss cheese. It appears entirely solid. However, it is full of holes�things you missed, things you misunderstood, things you did not quite catch. I know the knowledge feels solid, but it really is not. If you do not take action, those holes just get bigger as time passes and your memory begins to fade. Having taught for nearly 50 years, I know where the holes are likely to be. I can and will write test questions to expose those holes. In many ways, testing is just an attempt to measure the quantity and size of the holes ...

4 Ways to Promote Gender Equity in Your Classroom

February 20, 2018

By Jessica Deshler , West Virginia University There is something beautiful about the structure of mathematics that we can all appreciate, but it�s equally beautiful because it can be creative and messy. So is the teaching of mathematics. As mathematicians, we know and understand the complexities involved in our discipline, but sometimes overlook the underlying complexities of our classroom environment when preparing to teach. You�ve likely heard about the leaky pipeline � the phenomenon that describes the loss of women from STEM fields at various points in the academic pipeline. Because many undergraduate women leave the STEM pipeline after taking a mathematics course , our discipline can especially benefit from classroom practices known to help retain and support these students. You might wonder whether the gender breakdown in our classes or variation in our students� cultural and social backgrounds matter. We posit that these do matter, and that they can impact whether stu...

The One Question Calculus Final

January 23, 2018

By Lew Ludwig (Editor-in-Chief), Denison University As the semester begins and we prep for classes, the practice of backward course design is a powerful way to get the most of the learning experience for our students. With this in mind, I thought I would share one of my favorite exam questions for a first semester calculus course, which appears below. I call it �the one question calculus final.� Now of course this is tongue-in-cheek, as the one question has over 15 questions. Nonetheless, this one question tour de force covers the full range of a first semester calc course. To substantiate this bold claim, I found a comprehensive list of typical topics in such a course at Wolfram Mathworld Classroom . The chart below cross-references each alphabetically listed topic with its specific question. While some questions touch on a range of topics, the cross-referencing refers to the primary reference. Why I like this question: I really like this question because it requires...

UDL - The Great Unknown?

August 04, 2009

When you discover something that is personally tranformative, you share it with others; it's too difficult to keep it to yourself. And because I repeatedly observe teachers struggling with the challenge of how to reach all the learners in their classrooms, I am on a mission . I will do whatever it takes to teach others about UDL, or Universal Design for Learning because I believe UDL transforms teaching practices and makes learning possible for struggling learners. I can not keep this to myself. Recently, I had the opportunity to share about UDL at both NECC in DC, at the interactive UDL Playground and at EdubloggerCon East at BLC09 in Boston. I'm continually mystified by the reality that so few educators have heard about UDL and even fewer are applying the principles of offering multiple methods of engagement, presentation and expression to tap into students' affective, recognition and strategic networks to reach all learners. The connection between new media techn...

MAA IP Guide � Assessment

February 06, 2018

By Rick Cleary (guest blogger), Babson College A note from the Editors: This semester Teaching Tidbits will have several posts highlighting the new Instructional Practices Guide ( IP Guide ) from the Mathematical Association of America ( MAA ). The MAA has a long tradition of reporting what content should be taught in the mathematics classroom through its Curriculum Guide ; now the new IP Guide addresses how things could be taught in the mathematics classroom, how one could to design that experience, and how one could assess that experience. The suggested practices are well grounded in research on student learning. In our first post about the IP Guide, we dive deeper into the Assessment Practices section of the guide. Thanks to Rick Cleary, a lead writer for this section, for providing this post. The opening statement of the Assessment chapter of the MAA Instructional Practices guide makes the following claim: Effective assessment occurs when we clearly state high-quality goals for...

The Role of Failure and Struggle in the Mathematics Classroom

November 07, 2017

By Dana Ernst , Contributing Editor, Northern Arizona University The purpose of this post is to generate discussion and to get us thinking deeply about our teaching practices. This post introduces teaching concepts that researchers and educators developed to promote student success. In an attempt to understand who is successful and why, psychologist Angela Duckworth has spent years studying groups of people in a variety of challenging situations. Over and over again, one characteristic surfaced as a significant predictor of success: grit. According to Duckworth , grit is passion and perseverance for long-term goals. One of the big open questions in cognitive psychology is how to develop grit. Growth Mindset Research suggests that one of the key ingredients to fostering grit is adopting a growth mindset . Psychologist Carol Dweck defines growth mindset as the view that intelligence and abilities can be developed with effort. In contrast, a fixed mindset is the belief that one's ...

5 Ways to go Beyond Recitation

September 26, 2017

By E. Fuller , WVU Mathematics (guest blogger) Students at almost every institution of higher education will encounter a recitation as part of their mathematics class at some point, part of the class time set aside to repeat foundational mathematical equations. Graduate teaching assistants (GTAs) are frequently called on to lead these smaller groups of students through the basics of finding the roots of a quadratic equation or computing derivatives using the chain rule. Recitation time is often left for practice of the techniques students learn in lecture. But what if we could do more during this class time? What would that look like? Here are a few approaches you can take to change your students� experiences during recitation. 1) Focus on getting students to do the work instead of doing it for them. Homework problems are great and it�s sometimes easiest for us to go to recitation prepared to work out many variations of problems we�ve done ahead of time. The problem is that we alrea...

Here Is Your Assignment AND Words from a Legendary Teacher

August 04, 2015

My next set of classes starts on Monday, August 24. However, I emailed my students their first assignment back on April 28. I did not want them to waste their summer. More importantly, I wanted to start having a positive influence on them as soon as possible. The assignment had several parts culminating in their writing a short essay on the characteristics of a great student. I just wanted them to think about what that meant. I�ll write more about the results of that assignment during the fall when I see whether it had any impact on the students. Today, though, I want to give you an assignment to complete before your fall semester begins. When I put on teaching presentations, I often begin by instructing my audience to do the following exercise. Standing in front of all those teachers, I ask every person to close their eyes. (I always warn them that they cannot fall asleep.) ...

5 Free Apps to Use in the Classroom

January 17, 2017

By Julie Phelps , Contributing Editor, Valencia College Students have smartphones and want to use them all the time! My solution: well, if you can�t beat them, join them. With that in mind, I began looking for apps that can help facilitate learning. I want my students to use electronic devices for learning �good� and not as the �evil� learning detractors that we educators often perceive them to be. Here are some of my favorites to use in the classroom, plus one to keep an eye out for on your algebra students� screens. Kahoot! is a game-based classroom response system that uses quizzing to present content and generate discussion. The game can be displayed on a shared screen. Students can join the game on their own smart device/computer as long as they have a browser and a good internet connection. Quizizz is game-based tool similar to Kahoot!. With Quizizz you can randomize the questions to allow students to go at their own pace. The game also displays the correct answer when the...

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