A MATHCOUNTS competition question




Unexpected zeros error in MATLAB in zeros function


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YouTube Comment: This MATLAB program gives me an error.  W=2.4; L=3; Delta=0.6; i=(W./Delta)+2; j=(L./Delta); T=zeros(i,j); . When I write 0.1 for Delta, there is an error for zeros statement.

Answer: When writing a new program, avoid using the semicolon as it suppresses the output. Write each line separately in a .m file and run the mfile. That way you would have noticed that “i” is turning out to be a real number. It shows up as 26.0000 but if you use format long statement, you will see that you get 25.999999999999996. You can round(i) and round(j) to the nearest integer. The reason “i” turns out to be 25.999999999999996 is because of roundoff error, as numbers and calculations get represented in binary format.


Using Smart Sparrow as Clickers


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In Fall 2017, I will be using Smart Sparrow platform to improve the efficacy of the flipped classroom for pre-class learning.  I have been using clickers in the classroom for the last ten years and stumbled on this link  This link shows how to use Smart Sparrow to do polling in the class, and hence is an alternative to clickers for my class. This will save my students money and also save them from having to navigate another platform for use of personal response systems.  I will move the clicker questions over in Fall 2017 and use them in Spring 2018.  Yes, it is a long time from now, but you do not have to wait.

New Picture (1)


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Getting Started on Smart Sparrow Adaptive Platform


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May 13, 2017

Autar Kaw

We are developing content for a course in Numerical Methods on the Smart Sparrow adaptive platform. There is a learning curve for you to get started but it does not have to be difficult.  To get going, we propose the following.

  1. Watch this YouTube Smart Sparrow playlist to get an overview (22 minutes of video).
  2. This tutorial video will help you make your first lesson (52 minutes long).
  3. This tutorial from Learning Solutions magazine illustrates the authoring environment.
  4. The knowledge base for Smart Sparrow is an essential resource and I would concentrate just on the creating lessons part first.
  5. Then there is always the dependable support available by emailing to or by filling an online form.

In our future blogs, we will be illustrating our use of Smart Sparrow in the development of our lessons by creating tutorials based on generic content.


Prerequisite Example for Newton Raphson Method


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Flipped Learning and Active Learning are Not Synonymous

April 05, 2017

In an article titled The Hidden Costs of Active Learning by Thomas Mennalla, an associate professor of biology at Bay Path University, mentions that “Flipped and active learning truly are a better way for students to learn, but they also may be a fast track to instructor burnout.”  He starts his article – “I am an active learning college instructor and I’m tired. I don’t mean end-of-the-semester and need-some-sleep tired. I mean really, weary, bone-deep tired.”

I applaud the effort by Professor Manella as he is using effective evidence-based pedagogy, and I can relate to the burn-out when I first used the flipped classroom. However, I am personally concerned that flipped learning and active learning are considered to be somewhat synonymous.  We do not have to teach a class flipped to incorporate active learning.  Just small exercises at 15-minute intervals in a 50-minute class, like asking two to four clicker questions, a 25-word muddiest point essay, or something akin,  have been found to be effective.

I implore all my higher-ed colleagues and administrators not to push flipped classes just because that is the only way you know or have heard of incorporating active learning. Before embarking on a flipped class, try a blended class first with all the resources you would have developed for a flipped class; couple it with effective learning strategies like distributed practice (algorithmic problems and question banks presented through learning management systems will save you time to grade and curb cheating), giving practice tests, and assigning interleaved practice.

If someone has convinced you that flipped class (learning) is the only answer, ask them, “Have you compared it with a blended class where the active learning items done in class are of low cost – both for class time and professor prep time?”  Comparing the flipped class with the traditional lecture class should be seriously questioned as a research question.  The same meta-study which is quoted by many advocates of active learning and unrelatedly the “death of the lecture” tend to conveniently ignore the last sentence in its abstract – “The results raise questions about the continued use of traditional lecturing as a control in research studies, …..”

I teach my classes flipped as well as blended.  In the blended class, I have several in-class active learning exercises (clicker questions, short exercises, think-pair-share, etc), and therefore a reasonable amount of content has to be pushed out-of-class and online. Are they hence not getting the benefit of self-regulated and deep learning by doing that? Are they not using the group space during active learning exercises for “dynamic, interactive and engaging activities”?

Full Disclosure: I see the benefits of flipped learning but we do not have to flip every topic. Flipping does not have to create a burn-out either.  Even good medicine has to be taken in prescribed doses.  Currently, I am a lead PI on two NSF grants – one on comparing flipped and blended classes and another on using adaptive learning to improve the pre-class experience of flipped classes.  Let the data do the talking.


Why I do not allow cell phones or regular laptops in class



I do not allow cell phones and regular laptops in my class – it is considered academic disruption. If someone is expecting an important call, I ask them to let me know and sit in chairs close to the classroom exit door. Very few people take me on that offer over a semester even in a class of 109. “Loved ones including mine should call 911 in case of an emergency – the emergency response team will be there faster than we can.”

I do allow flat laptops and tablets only if they are used to take notes with a stylus. They cannot claim that they want to type notes as that is virtually impossible to do in an engineering course full of equations and sketches. Anyway, taking notes by hand is cognitively better than typing anyway.

About those of you who keep mentioning personal responsibility and that it is an ego trip for the instructor, how many studies do I need to show you about negative effects of multitasking and working memory when one is learning something new.

About personal responsibility, it is more than that – the cell phone distracts others and there are studies on that too.  And removing temptation is much better than self-control.

About those who say, be more interesting than the incoming text – I cannot compete, as learning something new is hard and looking at a “Facebook like” is an immediate high. My lecture is anticipated if I am doing a good job of constructing knowledge but a text is a Pavlov’s bell.


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Background Example for Newton Raphson Method


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One of the three tenets of a student succeeding in a course is how well he knows the pre-requisite knowledge for the course (other two tenets are ability and interest).  We as instructors can make it easier for students to get to a reasonable competency level by offering short reviews of the pre-requisite knowledge in form of video and/or text.

Here , a student will review via an example the background needed to learn Newton-Raphson method of solving a nonlinear equation of the form f(x)=0.

For more videos and resources on this topic, please visit


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Research Grant Offered to Improve Flipped Classroom through Adaptive Learning

Tampa, FL (December 20, 2016) – Ever since Autar Kaw started teaching at the University of South Florida in 1987, he has used evidence-based pedagogies such as interactive instructional software and active learning in the classroom.  Since 2001, he has been conducting federally funded research in transforming undergraduate engineering education through development and assessment of open resources for undergraduate courses such as Numerical Methods.

With his success of using blended learning for more than a decade and having been the lead developer of a comprehensive open courseware for Numerical Methods, the National Science Foundation (NSF) granted a four-institution (University of South Florida, Arizona State University, Alabama A&M, and University of Pittsburgh) grant in 2013 to determine the effectiveness of flipped learning classroom.  As per the Flipped Learning Network, “Flipped Learning is a pedagogical approach in which direct instruction moves from the group learning space to the individual learning space, and the resulting group space is transformed into a dynamic, interactive learning environment where the educator guides students as they apply concepts and engage creatively in the subject matter.”  The research from the grant indicated positive improvement in student learning gains through flipped learning but challenges persisted in some students coming inadequately prepared for the classroom meeting.  Although before class they were required to study through their preference of video lectures or textbook, and take an automatically-graded online quiz, it still was a single recipe prescribed for all.

To address this concern of pre-class preparation, NSF has given Professor Kaw and his colleague Professor Mary Besterfield-Sacre of University of Pittsburgh an Engaged Student Learning Exploration and Design grant that will use the adaptive platform of Knewton, Inc to personalize the pre-class activities for every learner.  Knewton’s mission is to support and challenge every student to meet their learning goals through personalized learning.

flippedclassroomuwcolorsTraditional vs Flipped Classroom (Photo Courtesy of University of Washington – Center for Teaching and Learning and Office of the Provost)

To improve the pre-class activities of the flipped class, the instructional and assessment modules from prior NSF support are being augmented and revised to conform to the Knewton adaptive platform. Specifically, the project will be comparing the effectiveness of three instructional approaches: a flipped class with adaptive learning, a flipped class without adaptive learning, and a blended class without adaptive learning, based on student conceptual gains, procedural knowledge, higher-order problem solving, and affective learning. These comparisons will be conducted statistically at a granular level using the factors of GPA, gender, race, age, transfer status, socioeconomic status, working hours, course topic, proficiency levels, and time on task, as well as qualitatively via focus groups and interviews.  This work will hence advance the understanding of the impact of the combined flipped and adaptive approaches on cognitive and affective learning gains of students representing diverse populations.

This project will specifically provide materials and best practices for teaching Numerical Methods in a flipped setting on an adaptive platform and provide new viable opportunities to how STEM courses are taught. This effort will also take us closer to meeting the NAE’s 21st Century Grand Challenge of “Advance Personalized Learning”.  Dissemination avenues include the freely-available Knewton adaptive platform, an open education resource portal from prior support, and social media.

For more information about the project, send an email to

Deriving trapezoidal rule using undetermined coefficients



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