Numerical Methods Guy

Is there a way to make up for the lack of time the student has but they have the attitude and ability? May 16, 2024.  Read blog.

Multiple Chance Testing as a Gateway to Standards-Based Grading, May 6, 2024. Read blog.

Should we get into a tizzy about students meeting deadlines, April 7,2024. Read blog.

Effect of Multiple Chance Testing on Student Performance and Perception, April 6,2024. Read blog.

How do I solve a first order ODE numerically in MATLAB? October 15,2023. Read blog.

Journal paper on use of adaptive learning in flipped classrooms published, August 28, 2023. Read blog.

Asking ChatGPT to look at my student evaluations to give me advice on improving my teaching, May 19, 2023. Read blog.

A VBA function for Cohen’s effect size, May 14,2023. Read blog.

Using PollEveryWhere in University of South Florida, January 18,2023. Read blog.

Balancing the social mobility index and reputation rankings, December 19,2022. Read blog.

Integrating functions given at discrete points via MATLAB, March 6,2022. Read blog.

Quick Start Guide to OpenMCR Program for a Single Key Exam, October 11, 2021. Read blog.

A multiple-choice question response reader, September 29, 2021. Read blog.

Getting last name and first name from full name with a delimited comma, September 11, 2021. Read blog.

A javascript code for Romberg integration, April 14, 2021. Read blog.

Removing YAML from an RMD file through an R script, March 10, 2021. Read blog.

Useful hints for a newbie on Rmarkdown, March 7, 2021. Read blog.

Converting a Word docx file to a draft R Markdown file, February 28, 2021. Read blog.

Canvas quiz times for accommodating students with disabilities, February 7, 2021. Read blog.

A prompt for students to write a discussion post on the most difficult topic in a chapter. January 2, 2021. Read blog.

How do I do that in MATLAB for USF students, December 22, 2020. Read blog.

Gaussian quadrature and weights listed as scrapeable data, October 31, 2020. Read blog.

Multiple Choice Analyzer, September 8, 2020. Read blog.

An Example of Doing Learner Introductions in an Online Class, September 2, 2020. Read blog.

 

How do I solve an initial value ODE problem in MATLAB? Updated for MATLAB 2020a, July 3, 2020.Read blog.

Using Microsoft Forms as a Personal Response System, June 13, 2020. Read blog.

How do I do that in MATLAB, May 8, 2020. Read blog.

Need help with programming in MATLAB, May 8, 2020. Read blog.

A short sample programming project to exhibit how to submit one, May 7, 2020. Read blog.

COVID19 Regression Model and Other Thoughts, March 28, 2020. Read blog.

How to Make a PDF file, March 26, 2020. Read blog.

How to PUBLISH in MATLAB, March 25, 2020. Read blog.

Ability to break long fprintf statements, March 23, 2020. Read blog.

On Making A Video Lecture on iPad and Uploading to YouTube, March 20, 2020. Read blog.

Why Do We Use Numerical Methods? March 15, 2020. Read blog.

Why Don’t I Allow (Not Ban) Use of Cell Phones in Class – An Open Letter to Students? January 28, 2020. Read blog.

How do I solve simultaneous linear equations given in equation form? Updated Matlab 2018b, January 22, 2020. Read blog.

How do I solve a nonlinear equation that needs to be setup – Updated to MATLAB 2018b, January 22, 2020. Read blog.

Solution to ordinary differential equations posed as definite integral, January 13, 2020. Read blog.

Student participant costs in NSF budgets counts as direct cost, December 4, 2019. Read blog.

Third Edition of Programming Textbook, November 25, 2019.Read blog.

The program to find the determinant of matrix, November 2, 2019. Read blog.

Time it takes to find a determinant, October 20, 2019. Read blog.

Stripping the tags from an HTML file, August 20, 2019. Read blog.

New site for the Numerical Method MOOC, July 29, 2019. Read blog.

Open Education Resource Repository Links, July 10, 2019. Read blog.

Maximizing the cross-section of a gutter, June 12, 2019. Read blog.

Using Watu quizzes and Latex in WordPress, May 18, 2019. Read blog.

Reducing ordinary differential equations to state variable matrix form, May 15, 2019. Read blog.

Matrix Algebra: Eigenvalues and Eigenvectors, March 30, 2019. Read blog.

Matrix Algebra: Adequacy of Solutions, March 12, 2019. Read blog.

Matrix Algebra: Gauss-Seidel Method, March 1, 2019. Read blog.

Synergistic Activities on NSF Proposals, February 27, 2019. Read blog.

Matrix Algebra: LU Decomposition Method, February 19, 2019. Read blog.

Matrix Algebra: Gaussian Elimination Method, February 9, 2019. Read blog.

Matrix Algebra: System of Equations, January 29, 2019. Read blog.

Adaptive learning improves the flipped classroom, January 22, 2019. Read blog.

Matrix Algebra: Unary Operations, January 19, 2019. Read blog.

Matrix Algebra: Vectors, January 8, 2019. Read blog.

Matrix Algebra: Binary Operations, December 25, 2018. Read blog.

Matrix Algebra: Introduction, December 17, 2018. Read blog.

Reporting results from prior NSF support when PIs on a proposal were PIs on a recent grant, November 30, 2018. Read blog.

An FE Math Problem in Analytical Geometry, November 5, 2018. Read blog.

An FE Exam Math Problem in Partial Differential Calculus, October 8, 2018. Read blog.

An FE Exam Math Problem in Ordinary Differential Equations, September 3, 2018. Read blog.

One Two, No Test Review, August 23, 2018. Read blog.

One, two, buckle my shoe, August 22, 2018. Read blog.

Fulbright Specialist Diary: Day 17 thru 18, August 8, 2018. Read blog.

Fulbright Specialist Diary: Day 16, August 7, 2018. Read blog.

Fulbright Specialist Diary: Day 14-15, August 6, 2018. Read blog.

Fulbright Specialist Diary: Day 12-13, August 5, 2018. Read blog.

Fulbright Specialist Diary: Day 11, August 4, 2018. Read blog.

Fulbright Specialist Diary: Day 10, August 3, 2018. Read blog.

Fulbright Specialist Diary: Day 9, August 2, 2018. Read blog.

Fubright Specialist Diary: Day 7 thru Day 8, August 1, 2018. Read blog.

Fulbright Specialist Diary: Day 6, July 31, 2018. Read blog.

Fulbright Specialist Diary: Day 5, July 30, 2018. Read blog.

Fulbright Specialist Diary: Day 4, July 28, 2018. Read blog.

Fulbright Specialist Program Diary: Day 1 to 3, July 27, 2018. Read blog.

An FE Exam Math Problem in Differential Calculus, July 5, 2018. Read blog.

An FE Exam Math Problem in Analytical Geomtery, May 31, 2018. Read blog.

An FE Exam Math Problem in Complex Algebra, May 2, 2018. Read blog.

How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2. April 2, 2018. Read blog.

Euler’s Method Example for FE Exam, March 26, 2018. Read blog.

Computational Time for Forward Elimination Steps of Naive Gaussian Elimination on a Square Matrix, February 21, 2018. Read blog.

Global truncation error in Euler’s method, January 24, 2018. Read blog.

Resources for Numerical Methods, January 8, 2018. Read blog.

Local truncation error is approximately proportional to square of step size in Euler’s method, January 2, 2018. Read blog.

I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]? November 25, 2017. Read blog.

Converting a date to acceptable format in excel, October 1, 2017. Read blog.

Badges added to MOOC courses, August 27, 2017. Read blog.

Covariance between residuals and predictor variable is zero for a linear regression model. July 19, 2017. Read blog.

Sum of the residuals for the linear regression model is zero. July 6, 2017. Read blog.

A MATHCOUNTS problem solution via abstraction, June 26, 2017. Read blog.

Unexpected zeros error in MATLAB in zeros function, June 3, 2017. Read blog.

Using Smart Sparrow as Clickers, May 24, 2017. Read blog.

Getting Started on Smart Sparrow Adaptive Platform, May 13, 2017.  Read blog.

Prerequisite Example for Newton Raphson Method, April 18, 2017. Read blog.

Flipped Learning and Active Learning are Not Synonymous, April 6, 2017. Read blog.

Why I do not allow cell phones or regular laptops in class, March 14, 2017. Read blog.

Background Example for Newton Raphson Method, February 23, 2017. Read blog.

Research Grant Offered to Improve Flipped Classroom through Adaptive Learning, December 20, 2016. Read blog.

Deriving trapezoidal rule using undetermined coefficients, November 22, 2016. Read blog.

Implications of diagonally dominant matrices, November 4, 2016. Read blog.

WordPress does not update image, October 21, 2016. Read blog.

Clearing up the confusion about diagonally dominant matrices – Part 4, October 14, 2016. Read blog.

Clearing up the confusion about diagonally dominant matrices – Part 3, October 6, 2016. Read blog.

Clearing up the confusion about diagonally dominant matrices – Part 2, October 1, 2016. Read blog.

Clearing up the confusion about diagonally dominant matrices – Part 1, September 23, 2016. Read blog.

MOOC Released:Introduction to Numerical Methods – Part 2 of 2, September 14, 2016. Read blog.

Unresolved CANVAS LMS bug in algorithmic quizzes, June 17, 2016. Read blog.

A MOOC on Numerical Methods Released, April 5, 2016. Read blog.

Rejecting roots of nonlinear equation for a physical problem? February 12, 2016. Read blog.

End of semester grading VBA module, December 21, 2015. Read blog.

A quadrature formula example, November 9, 2015. Read blog.

Example to show that a polynomial of order n or less that passes through (n+1) data points is unique. November 4, 2015. Read blog.

Why multiply possible form of part of particular solution form by a power of the independent variable when solving an ordinary differential equation, October 5, 2015. Read blog.

Largest number that can be stored in a floating word of 7 bits, September 2, 2015. Read blog.

MOOC on Introduction to Matrix Algebra released, February 7, 2015. Read blog.

A Floating Point Question Revisited, February 6, 2015. Read blog.

Patriots football deflation given as a lesson learned and as an exercise in Numerical Methods, February 1, 2015. Read blog.

2014 in review, December 29, 2014. Read blog.

An example of Gaussian quadrature rule by using two approaches, December 3, 2014. Read blog.

Open course ware for Matrix Algebra Released, November 14, 2014. Read blog.

Friday October 31, 2014, 11:59PM EDT, November 1, 2014 3:59AM GMT – Release Date for an Opencourseware in Introduction to Matrix Algebra, August 5, 2014. Read blog.

Machine epsilon – Question 5 of 5, July 15, 2014. Read blog.

Repeated roots in ordinary differential equation – next independent solution – where does that come from? July 9, 2014. Read blog.

Machine Epsilon – Question 4 of 5, July 1, 2014. Read blog.

Machine epsilon – Question 3 of 5, June 20, 2014. Read blog.

Machine epsilon – Question 2 of 5, June 11, 2014. Read blog.

Machine epsilon – Question 1 of 5, June 4, 2014. Read blog.

A Facebook Page for Numerical Methods, December 29, 2013. Read blog.

Reconciling secant method formulas, October 1, 2013. Read blog.

A Grant to Study Flipped (Inverted) Classrooms, September 5, 2013. Read blog.

Inverse Factorial, August 26, 2013. Read blog.

The Learning Management System Canvas (Instructure) Lacks Key Feature in Quizzes, June 8, 2013. Read blog.

A MOOC on Introduction to Numerical Methods, June 5, 2013. Read blog.

The decimal point display in TI30Xa calculators, May 7, 2013. Read blog.

Misconceptions about diagonal and tridiagonal matrices, March 30, 2013. Read blog.

Making sense of the Big Oh! January 30, 2013. Read blog.

Using Taylor polynomial to approximately solve an ordinary differential equation, January 22, 2013. Read blog.

2012 in review, December 30, 2012. Read blog.

Proving the denominator of the linear regression formula for its constants is greater than zero. October 7, 2012. Read blog.

Prove that the least squares general straight-line model gives the absolute minimum of the sum of the squares of the residuals? September 3, 2012. Read blog.

Effect of Significant Digits: Example 2: Regression Formatting in Excel, August 19, 2012. Read blog.

Effect of Significant Digits: Example 1: Beam Deflection, August 5, 2012. Read blog.

Length of curve, June 28, 2012. Read blog.

Example: How many significant digits are correct in my answer? May 25, 2012. Read blog.

How many significant digits are correct in my answer? May 16, 2012. Read blog.

Do we have to setup all 3n equations for the n quadratic splines for (n+1) data points? March 24, 2012. Read blog.

Checking if a number is non-negative or not? March 4, 2012. Read blog.

Largest integer that can be represented in a n-bit integer word, February 15, 2012. Read blog.

Printer cuts off MATLAB code and text, January 28, 2012. Read blog.

Differentiating a Discrete Function with Equidistant Points, January 19, 2012. Read blog.

2011 in review, December 31, 2011. Read blog.

Saylor Foundation Harnesses Numerical Methods Resources, December 17, 2011. Read blog.

codecademy.com looks promising, November 30, 2011. Read blog.

Audiovisual Lectures for Novice Programmers, November 25, 2011. Read blog.

Livescribe, September 12, 2011. Read blog.

Does the solve command in MATLAB not give you an answer? September 8, 2011. Read blog.

Computational Time to Find Determinant Using Gaussian Elimination, August 21, 2011. Read blog.

Does the solve command in MATLAB not give you an answer? August 7, 2011. Read blog.

Computational Time to Find Determinant Using CoFactor Method, July 21, 2011. Read blog.

A MATLAB program to find quadrature points and weights for Gauss-Legendre Quadrature rule, July 7, 2011. Read blog.

YouTube Videos on Numerical Methods Cross 1-Million Views Mark, June 27, 2011. Read blog.

A Wolfram demo on how much of a floating ball is under water, June 14, 2011. Read blog.

Order of accuracy of central divided difference scheme for first derivative of a function of one variable, June 2, 2011. Read blog.

A Wolfram demo on converting a decimal number to floating point binary representation, May 24, 2011. Read blog.

A Wolfram Demo for Numerical Differentiation, May 10, 2011. Read blog.

Taylor Series in Layman’s terms, April 29, 2011. Read blog.

Computational Time for Forward Substitution, April 14, 2011. Read blog.

Computational Time for Back Substitution, March 30, 2011. Read blog.

Taylor Series Exercise – Method 3, March 11, 2011. Read blog.

Taylor Series Exercise – Method 2, March 2, 2011. Read blog.

Taylor Series Exercise – Method 1, February 17, 2011. Read blog.

Example: Solving a first order ODE by Laplace transforms, February 3, 2011. Read blog.

Classical Solution Technique to Solve a First Order ODE, January 21, 2011. Read blog.

Example: Solving First Order Linear ODE by Integrating Factor, January 7, 2011. Read blog.

2010 in review, January 2, 2011. Read blog.

Reading an excel file in MATLAB, December 14, 2010. Read blog.

Inverse error function using interpolation, October 4, 2010. Read blog.

Using int and solve to find inverse error function in MATLAB, September 1, 2010. Read blog.

Finding the inverse error function, August 24, 2010. Read blog.

Solving a polynomial equation for the longest mast problem? July 4, 2010. Read blog.

A real-life example of having to solve a nonlinear equation numerically? June 10, 2010. Read blog.

Converting large numbers into floating point format by hand, May 25, 2010. Read blog.

Does it make a large difference if we transform data for nonlinear regression models, April 15, 2010. Read blog.

To prove that the regression model corresponds to a minimum of the sum of the square of the residuals, April 8, 2010. Read blog.

A short online quiz for the MATLAB conditional statements, March 9, 2010. Read blog.

A short online quiz on the for-end loops in MATLAB, February 28, 2010. Read blog.

A video tutorial on Simpson’s 1/3 rule, February 23, 2010. Read blog.

A short online quiz on MATLAB basics, January 30, 2010. Read blog.

How do I read data from a textfile in MATLAB? November 29, 2009. Read blog.

MATLAB code for bubble sort, November 8, 2009. Read blog.

Bubble sorting, November 3, 2009. Read blog.

How do I numerically solve an ODE in MATLAB? October 20, 2009. Read blog.

The continue statement in MATLAB, October 16, 2009. Read blog.

The break statement in MATLAB, October 13, 2009. Read blog.

Are software bugs categorised as “that is the way it is”, September 24, 2009. Read blog.

You can watch the numerical methods videos on a mobile device, September 16, 2009. Read blog.

How do I solve simultaneous linear equations given in equation form? August 21, 2009. Read blog.

How do I solve a set of simultaneous linear equations given in matrix form? August 12, 2009. Read blog.

How do I do polynomial regression in MATLAB? August 3, 2009. Read blog.

How do I display the data of an array in MATLAB? July 8, 2009. Read blog.

Poems on Numerical Methods, July 4, 2009. Read blog.

How do I do spline interpolation in MATLAB? June 20, 2009. Read blog.

How do I do polynomial interpolation in MATLAB, June 11, 2009. Read blog.

How do I solve a boundary value ODE in MATLAB? May 25, 2009. Read blog.

How do I solve an initial value ODE in MATLAB? May 14, 2009. Read blog.

How do I solve a nonlinear equation that needs to be setup in MATLAB? April 17, 2009. Read blog.

How do I solve a nonlinear equation in MATLAB? April 11, 2009. Read blog.

How do I integrate a discrete function in MATLAB? April 3, 2009. Read blog.

How do I integrate a continuous function in MATLAB, March 28, 2009. Read blog.

How do I differentiate in MATLAB? March 21, 2009. Read blog.

Numerical Methods YouTube Video Progress, March 14, 2009. Read blog.

MATLAB code for the efficient automatic integrator, March 5, 2009. Read blog.

An efficient formula for an automatic integrator based on trapezoidal rule, February 28, 2009. Read blog.

Why keep doubling the segments for an automatic integrator based on Trapezoidal rule? February 23, 2009. Read blog.

A problem using central divided difference error order, February 9, 2009. Read blog.

Audiovisual Lectures on Numerical Methods, January 27, 2009. Read blog.

Proper modeling needs to precede numerical solutions, January 15, 2009. Read blog.

Numerical Methods Book Printed, January 8, 2009. Read blog.

Is a square matrix strictly diagonally dominant? November 29, 2008. Read blog.

Skipping numbers in picking the lotto numbers, November 21, 2008. Read blog.

Is a square matrix diagonal or not? November 16, 2008. Read blog.

Picking lotto numbers, November 10, 2008. Read blog.

Comparing two series to calculate pi, October 30, 2008. Read blog.

An automatic integrator using Trapezoidal rule, October 19, 2008. Read blog.

Another improper integral solved using trapezoidal rule, October 8, 2008. Read blog.

The BMI (Body Mass Index) Program, September 28, 2008 .Read blog.

Experimental data for the length of curve experiment, September 21, 2008. Read blog.

A better way to show conversion of decimal fractional number to binary, September 14, 2008. Read blog.

Finding height of atmosphere using nonlinear regression, September 6, 2008. Read blog.

A better way to show decimal to binary conversion, August 30, 2008. Read blog.

Accuracy of Taylor series, August 23, 2008. Read blog.

Taylor series example, August 19, 2008. Read blog.

Taylor Series Revisited, August 11, 2008. Read blog.

Runge-Kutta 2nd order equations derived, August 7, 2008. Read blog.

A Matlab program for comparing Runge-Kutta methods, August 4, 2008. Read blog.

Example to show how numerical ODE solutions can be used to find integrals, July 31, 2008. Read blog.

Comparing Runge-Kutta 2nd order methods, July 28, 2008. Read blog.

Can I use numerical solution of ODE techniques to do numerical integration? July 25, 2008. Read blog.

Time of death – a classic ODE problem, July 21, 2008. Read blog.

Is it just a coincidence – true error in multiple segment Trapezoidal rule gets approximately quartered as the number of segments is doubled? July 18, 2008. Read blog.

Can I use Trapezoidal rule to calculate an improper integral? July 16, 2008. Read blog.

A metric for measuring wildness of a college football season, July 14, 2008. Read blog.

Experiment for spline interpolation and integration, July 11, 2008. Read blog.

Abuses of regression, July 9, 2008. Read blog.

How do you know that the least squares regression line is unique and corresponds to a minimum, July 7, 2008. Read blog.

Finding the optimum polynomial order to use for regression, July 5, 2008. Read blog.

Data for aluminum cylinder in iced water experiment, July 3, 2008. Read blog.

In regression, when is coefficient of determination zero, July 1, 2008. Read blog.

Length of a curve experiment, June 29, 2008. Read blog.

A legend used in the movie “The Happening”, June 27, 2008. Read blog.

Shortest path for a robot, June 25, 2008. Read blog.

Do quadratic splines really use all the data points? June 23, 2008. Read blog.

Extrapolation is inexact and may be dangerous, June 20, 2008. Read blog.

Finding the length of curve using MATLAB, June 18, 2008. Read blog.

A simple MATLAB program to show that High order interpolation is a bad idea, June 16, 2008. Read blog.

High order interpolation is a bad idea? June 14, 2008. Read blog.

If a polynomial of order n or less passes thru (n+1) points, it is unique! June 10, 2008. Read blog.

So what does this mean that the computational time is proportional to some power of n in Gaussian Elimination method? June 9, 2008. Read blog.

An experiment to illustrate numerical differentiation, integration, regression and ODEs, June 7, 2008. Read blog.

Rusty on Matrix Algebra, June 5, 2008. Read blog.

LU Decomposition takes more computational time than Gaussian Elimination! What gives? June 4, 2008. Read blog.

Round off errors and the Patriot missile, June 2, 2008. Read blog.

Myth: Error caused by chopping a number is called truncation error, May 27, 2008. Read blog.

Undergraduate Numerical Methods for Engineering, May 26, 2008. Read blog.

 

 

 

Many students consider optimal approaches for effective learning. Often, preferences are influenced by cognitive comfort, akin to the appeal of ultra-processed foods, whereas more effective strategies, though less comfortable, resemble the benefits of fresh food.

Enhancing student achievement depends not only on what is learned but also on how it is studied. In his comprehensive article (an extended article is also available), psychologist John Dunlosky critiques the prevalent use of suboptimal study habits such as highlighting, rereading, and cramming. He advocates for evidence-based methods that significantly improve learning outcomes across various age groups and disciplines.

Foremost among these are practice testing and distributed practice. Practice testing, which involves self-quizzing or completing mock exams, strengthens memory and comprehension through active recall. Distributed practice, characterized by spacing study sessions over time, has been shown to increase long-term retention compared to last-minute cramming.

Additional effective techniques include interleaved practice (alternating between different types of problems), elaborative interrogation (asking “why” questions to enhance understanding), and self-explanation (relating new knowledge to existing knowledge). These approaches foster deeper cognitive engagement and superior problem-solving abilities.

In contrast, widely used strategies like highlighting, rereading, and summarizing are largely ineffective unless integrated with more active learning methods. While these practices may appear productive, research indicates they yield minimal enduring benefit.

Dunlosky’s findings underscore the importance of instructing students in effective learning strategies alongside subject content. Providing learners with practical, research-backed study techniques enables them not only to perform well academically but also to cultivate skills essential for lifelong learning.

Read the extended version.

Read the brief version

---

This post is brought to you by

• Holistic Numerical Methods Open Courseware:
  • Numerical Methods for the STEM undergraduate at https://nm.MathForCollege.com;
  • Introduction to Matrix Algebra for the STEM undergraduate at https://ma.MathForCollege.com
• the textbooks on
  • Numerical Methods with Applications
  • Introduction to Programming Concepts Using MATLAB
• the Massive Open Online Course (MOOCs) available at
  • Numerical Methods 
  • Introduction to Matrix Algebra

In a 50-page paper, “The Memory Paradox: Why Our Brains Need Knowledge in an Age of AI“, the authors examine the paradox related to human memory during the advancement of artificial intelligence. While AI grants significant access to information, it may also impact cognitive abilities essential for in-depth analysis and learning. The authors suggest that heavy dependence on digital tools can impact internal memory systems and lead to a surface-level understanding of knowledge. They propose a balanced model that merges technological tools with traditional educational methods to promote critical thinking and memory retention. This summary outlines the key points from the paper.

The role of human memory is examined in the context of artificial intelligence’s capacity to recall facts, solve problems, and generate content. The paper argues that while digital tools offer substantial information availability, they may also alter cognitive skills essential for reasoning and practical learning.

A key topic is cognitive offloading, that is, the use of external tools to reduce mental effort. While this strategy can be helpful for complex tasks or minor details, the authors note that over-reliance on such tools can influence the way individuals store and access information. Instead of forming comprehensive mental models, people may remember where information is located rather than its content, resulting in what is described as an “illusion of knowledge.” This phenomenon can lead to the perception of being informed without a thorough understanding of the underlying concepts.

Neuroscientific research is referenced to explain how prediction errors, discrepancies between expectations and outcomes, are essential for establishing memory traces and enhancing neural connections. The lack of initial internalization of knowledge hinders the ability to make predictions, which are crucial to learning, thereby impacting the development of comprehension and intuition.

The paper discusses educational trends, noting that some schools have shifted away from memorization towards teaching methods centered on critical thinking and discovery learning. The increased reliance on external resources coincides with observed declines in IQ scores in various regions, a reversal of the earlier Flynn Effect. The authors associate these patterns with educational practices that place less emphasis on memory and more on external aids.

With the growth of generative AI tools such as ChatGPT, these concerns are considered more pertinent. Studies cited in the paper indicate that students who depend heavily on such tools may spend less time reflecting, self-correcting, and retaining new information. This dependence has been referred to as “metacognitive laziness,” implying a tendency to avoid the mental effort required for lasting learning outcomes.

The suggested approach is to integrate technology thoughtfully, using AI to enhance, not replace, cognitive processes. The paper emphasizes the importance of retaining fundamental knowledge for critical thinking, error identification, and efficient acquisition of new information. A balanced strategy, including desirable difficulty, retrieval practice, and internalizing key knowledge, is recommended. It is noted that students benefit from challenges set at an appropriate level to stimulate engagement without causing undue frustration.

In conclusion, the memory paradox raises questions about learning approaches in the context of widespread digital technology. The paper concludes that although technology expands capabilities, it does not eliminate the need for mental effort in understanding material. Retaining knowledge internally remains crucial, as the ability to remember, reason, and reflect continues to play a vital role in navigating complex and information-rich environments.

---

This post is brought to you by

• Holistic Numerical Methods Open Courseware:
  • Numerical Methods for the STEM undergraduate at https://nm.MathForCollege.com;
  • Introduction to Matrix Algebra for the STEM undergraduate at https://ma.MathForCollege.com
• the textbooks on
  • Numerical Methods with Applications
  • Introduction to Programming Concepts Using MATLAB
• the Massive Open Online Course (MOOCs) available at
  • Numerical Methods 
  • Introduction to Matrix Algebra

Our paper was finally published.

Citation: A. Kaw, A. Yalcin, R.M. Clark, R.B. Gomes, L. Serrano, A. Scott, Y. Lou, “On Building and Implementing Adaptive Learning Platform Lessons for Pre-Class Learning in a Flipped Course,” ASEE Computers in Education, Vol 14 (2), 2024,1-23.

Link: https://coed.asee.org/wp-content/uploads/2025/01/VOL14_Issue2-P1-Final.pdf

Abstract: Research shows active learning improves student performance and narrows the achievement gaps for marginalized groups. One of the active learning strategies is the use of flipped learning. However, flipped classrooms pose challenges due to reluctant student preparation in the pre-class learning requirements and general resistance from students to the modality. To address these challenges for a flipped engineering course in Numerical Methods, adaptive learning lessons that present content, assessment, and feedback based on student engagement and performance were created using a commercial platform for pre-class learning. The paper details how the lessons were developed, implemented in pre-class learning, and revised, creating a framework for other engineering educators who may want to duplicate them. An initial study of student behavior during the lessons showed that a low-performing student made many more attempts at the assessments while spending less time on the accompanying learning materials.

Introduction

• • • The paper discusses the development and implementation of adaptive learning platform (ALP) lessons for pre-class learning in a flipped engineering course on Numerical Methods.
    • The aim is to address challenges in flipped classrooms, such as student reluctance to prepare for pre-class learning and resistance to the flipped learning modality.

Background

• • • Active learning has been shown to improve student performance and narrow achievement gaps for marginalized groups.
    • Flipped learning involves moving direct instruction from group learning space to individual learning space, transforming the group space into an interactive learning environment.

Development of ALP Lessons

• • • The ALP lessons were developed using the RealizeIT commercial platform.
      The lessons were created to provide personalized and flexible learning by monitoring student progress and performance.
    • The course topics were broken down into individual objectives and nodes, with each node including sections such as introduction, learning objectives, video lectures, textbook content, and assessment.

Implementation and Testing

• • • The ALP lessons were implemented and tested in the classroom during Spring 2021.
    • The lessons accounted for 15% of the student’s final course grade and were linked via the CANVAS learning management system.
    • The ALP lessons followed W3C accessibility standards and included features like transcripts for videos and alternative textbook content.

Student Interaction and Behavior

• • • The paper presents a case study of student interactions with a specific node in the ALP lessons.
    • Data on student engagement, activity duration, and performance were collected and analyzed.
    • The study found distinct differences in how students with different final course grades interacted with the ALP lessons.

Revisions and Improvements

• • • Feedback from students and instructors was used to revise and improve the ALP lessons.
    • Revisions included re-recording video lectures in HD quality, converting textbook content to HTML format, and adding intermediate answers for algorithmic questions.

Conclusion

• • • The paper concludes that adaptive learning lessons can effectively improve student preparation and engagement in flipped classrooms.
    • The authors suggest that recognizing unique student behaviors can inform study habits and guide in-class exercises and mini-lectures.

A professor wrote in a newsletter: “However, many students are taking on too much, doing more than one ‘full-time’ thing: paid work, university courses, and other responsibilities. Many students who have the attitude and ability to succeed don’t have the time and energy needed to achieve their best.”

The question that followed was whether there was a way to make up for the lack of time the student has.

• • • I know some people who favor mastery grading might not agree, but I think giving endless quizzes is not fair for such students.
    • But seriously, keep the graded components low stakes (does not discourage) and simple, e.g., three midterms, a final exam, weekly online HW that is formative (give multiple tries) but be low time consuming and challenging enough to keep that distributed practice going. Do not require attendance. After all, we are assessing learning – right.
    • How much they are working should not affect how students get graded – surely how you support students though is important
    • I offer free one-on-one tutoring of one hour a week (not many takers – less than 10% of the class).
    • Office hours are also held outside of the 8-5 time, and can be face to face or online as per their preference.
    • I also answer course content emails quickly.
    • Universal Design for Learning (UDL), which is a framework to accommodate diverse learners, I have let students in some courses choose between a final examination or a culminating project. The former takes less time to prepare but can be hard to ace, the latter takes more time but is easier to ace.

 

Multiple Chance Testing as a Gateway to Standards-Based Grading 

Autar Kaw

May 6, 2024

Traditional grading may not reflect student learning, which is a common concern. Imagine a large enrollment class that assesses learning via three midterm tests and a final exam, each weighing 25% of the semester grade. If a student scores 46%, 90%, 90%, and 90% on the four assessments, they will have a grade of C at the end of the semester. What are the alternatives? Some speak of using standards-based grading (SBG).  So, what is SBG? 

What is SBG? 

Standards-based grading (SBG) is an alternative method of assessing students. It emphasizes evaluating their mastery of specific learning objectives or standards rather than using points or percentages for assignments and exams. In SBG, students receive feedback on their progress toward each standard and are given multiple opportunities to demonstrate their proficiency. The goal of SBG is to foster a growth mindset where students view learning as a process of improvement rather than a competition for grades. 

My reservations about adopting SBG 

I considered using SBG in my Numerical Methods class, a required junior-level course in Mechanical Engineering at the University of South Florida. The class typically enrolls 60-120 students per semester.  I started watching YouTube videos, reading blogs, and analyzing journal papers on SBG. As I reviewed the many ways instructors use SBG, the idea of implementing it into my courses seemed overwhelming. Some had 30-50 standards in a course, and keeping track of each standard for every student would be overwhelming for students as well as the instructor.  

Some instructors were using short quizzes for each standard. Others asked students to master pre-class work, take in-class quizzes, do online homework, and complete short projects. But what happens when they do not master a standard the first time? They can show proficiency via retaking a quiz in specific quiz sessions held during class time, office hours, final exam sessions, etc.  

How many chances does each student get to show proficiency in a standard? How does the instructor have quizzes ready to check any standard a student asks for, or is it the same quiz as the one given the first time? Does the latest proficiency level replace all previous ones, or is the highest proficiency used? As per SBG philosophy, it should be the latest score, but many choose the highest. Another tenet of SBG is equity, but how about the student who cannot make it outside of class time, such as office hours, to show proficiency – they may be taking other classes, working off-campus, or caring for a loved one or children? What happens to the class time lost used for re-quizzing? Does it lessen the content covered in the course and reduce the student engagement opportunities for active learning? 

Also, since we still use traditional letter grades on transcripts, proficiency in meeting standards must be converted to letter grades during and at the end of the semester. Our students expect to know where they stand during the semester by a total score or letter grade. However, the grade would be complicated for the instructor to calculate as well as the student to follow during the semester, as the grading system involves some combination of having shown a certain level of proficiency in each assessment category, such as pre-class work, quizzes on mandatory and secondary standards, online homework and projects. Not only that, but there is also no average grade during the semester, as one must meet a certain number of standards to get a particular grade, and enough standards have not been covered until one is toward the end of the semester. 

However, just because a system is imperfect does not mean one should abandon SBG. Can we adopt a system that would maintain the essence of SBG but be less daunting for a large class and less challenging for students and the instructor? 

Standards-Based Testing with a Twist 

I used a subset of SBG called standards-based testing (SBT), and within that framework, I used multiple-chance testing (MCT) on the midterms and online quizzes with some twists.  

The traditional grading system in the course comprised 15% of the learning-management system (LMS) quizzes, three 15% midterm tests, 10% for projects, 5% for a concept inventory, and 25% for a final exam. We used MCT for the LMS quizzes and midterm tests, which is 60% of the grade. In addition, the final exam, a standalone grading component, also counts as another chance test. 

The course was divided into eight standards, each a chapter. This division clearly delineated the standard for the student.  

There are 30 LMS quizzes in the semester. Each quiz has three questions, two of which are multiple-choice and one algorithmic. These questions were chosen using question banks I have developed for the course. The students can make as many attempts as they wish before the weekly deadline, and the LMS automatically reports the highest score. If they wanted to attempt them again after the deadline, they could do so till the last day of class and recoup half of the missed grade, e.g., if they scored 6/10 before the deadline and 9/10 after the deadline, their score would be 6+(9-6)/2=7.5/10. If their score after the deadline was lower, their grade on a quiz stayed unchanged. 

The semester has three midterm tests, which check 3, 3, and 2 standards, respectively. Checking for multiple standards in a midterm maintains the interleaving effect, where students must figure out which standard the question belongs to. Higher-order thinking exercises can also be given where one standard is a prerequisite for another. Each standard is graded out of 20 or 40 points depending on the length of the chapter. For example, Standard 1 is a 2-week long chapter and is graded out of 40, while Standard 2 is a 1-week long chapter and is graded out of 20. The score for each standard is reported on the graded test. Triple feedback is given to the student on each question asked – the wrong answer is pointed out, how to get to the correct answer is shown, and, more importantly, reference is given to examples and problems the student can attempt to review the material. Students were encouraged to come to office hours for face-to-face or online help. 

A second-chance test was given two to three weeks after each of the three mid-term tests. The student could take the retest on any or all the standards of the midterm test that they had just taken. For example, in midterm test one, we had three standards. The retest was given for three standards as separate tests of 25 minutes each (e.g., individual tests were given for Standard 1 from 11 AM to 11:25 AM, 5-minute break, Standard 2 from 11:30 AM to 11:55 AM, 5-minute break, Standard 3 from 12 noon to 12:25 PM). A late policy was implemented that if a student left early during a retest of a standard, a student coming in later than the first person leaving could not take the test. This policy was adopted to maintain the academic integrity of the retest, but we did not need to use it. We also posted the retests on the LMS for students so that they do not just show up to get a copy of the retest.  

The student could recoup only half of the missed points, e.g., if they scored 24/40 in the midterm test on Standard 1 and 34/40 in the retest, their score would be 24+(34-24)/2=29/40. If their score in the retest was lower, they were not penalized, and their grade stayed unchanged. If a retest for a standard was taken, the updated score was also limited to 90%. This policy was adopted to avoid highly performing students taking the retest for just gaining a few more points, as their time would be better spent learning new course topics. Although it was not my intention, this policy helped reduce grading efforts. Only 60% of the possible retests were taken in the course. 

The final exam was a standalone category in the grade but also a proxy for a third-chance test for all eight standards. Questions from the final exam were allocated to each standard, and the scores were used as third-chance test scores. The scoring update policy was the same as for the second-chance tests. Some would argue that I should have used the final exam session to test for standards that the students wished to get retested in, but the effect of the final exam on long-term retention must not be ignored.  

Since we did not have an uncomplicated way to report updated grades to the students, we made a student-friendly Excel spreadsheet where students could enter their grades for all the quizzes and tests they had taken. The spreadsheet calculated the grade without and with the retests. The grade without the retests matched the overall grade reported on the LMS, so students knew their minimum grade at any time in the semester if they did not want to use the Excel spreadsheet. To calculate the final grade, one needs to get the grades from their LMS and use simple spreadsheet functions, but this process can then be automated for later semesters. 

The findings when comparing a course with MCT to that without 

We compared the student performance and affective outcomes for the course with and without MCT. The findings reported in a journal paper indicated that implementing MCT resulted in a higher percentage of students achieving a high final exam score (15% vs. 3%), a more considerable proportion of ‘A’ grades (36% vs. 27%), and a more positive classroom environment in terms of participation, unity, and satisfaction. During focus groups, students appreciated the enhanced learning experience, the opportunity for retakes, and the reduced stress associated with standards-based testing. A few mentioned the issue of not knowing their ongoing grade in the course. The journal article cited below provides more details of the study’s results.  

My questions to the reader are: Would you use multiple-chance testing? How would you implement it differently? How can you maximize the advantages of MCTs and minimize the drawbacks for students and instructors? Do you have a better way of reporting grades in LMS so that the current overall grade is reflected just in time? 

References: Autar Kaw and Renee Clark, Effects of Standards-Based Testing via Multiple-Chance Testing on Cognitive and Affective Outcomes in an Engineering Course, International Journal of Engineering Education, Vol. 40, No. 2, pp. 303–321, 2024, https://www.ijee.ie/latestissues/Vol40-2/09_ijee4434.pdf.

April 7, 2024

In a recent paper on extending deadlines for student assignments, researchers point out that it is not an issue we need to sweat about.

“This study uses evidence to debunk common misconceptions about assignment extensions.”
“The extension without penalty system was used by 78% of the students, but half of them only used it once”

My two cents: There is always a happy medium between being strict and lenient. Extending deadlines for everyone is fair—not just for those who ask unless they have a reasonable excuse. Many extroverts get ahead because they ask—are we rewarding behavior or learning? Sure, one should also give a fixed number of unexcused deadline extensions so that private issues are not forced to be exposed.

In LMS, one can set a deadline and then “open until” a date. The two can act as deadlines and extended deadlines, respectively. I did this for a few assignments in a course many years ago, and the “open until” became the deadline, and it was all the same. Students catch up fast, and it makes no difference. Less than 10% of the students submitted on time. The extended deadline bugs students though, as the “open until” does not show up on their calendar, and they must manually keep track of deadlines – oh, the travesty.