Contributor: Michael Lafreniere, Ohio University-Chillicothe.

Student learning can be assessed, but how do we make visible the learning process so as to ensure that student learning is aligned with our mathematical learning objectives as they pertain to conceptual understanding? This alignment (or fidelity) of student learning can be addressed with terms such as cognitive fidelity and mathematical fidelity.

Cognitive fidelity is seeing accurately what thoughts, concepts, and connections occur in the mind.

Mathematical fidelity is a tool’s ability to represent mathematics accurately (symbolically, graphically, etc.).

Enhanced WebAssign is a digital assessment tool equipped with the characteristics to make student learning visible at a high level of cognitive and mathematical fidelity. Enhanced WebAssign provides high mathematical fidelity. The tools available to both teacher and student include Mathematica computer algebra system capabilities and graphical features. These allow students to reach beyond multiple-choice options and symbolically convey their mathematical thoughts. In terms of cognitive fidelity, the Show My Work and Pencil Pad within Enhanced WebAssign allow students to elaborate their thinking, thereby, making visible their level of conceptual understanding.

As a teacher, I am interested in my students taking the time to show their work so they can convey the concepts of their mathematical learning. With the time savings

afforded and quick student feedback with Enhanced WebAssign’s automated symbolic grading, I am able to efficiently and with high levels of fidelity collect my students’ thinking. To do this, I use both the Show My Work and PencilPad features of EWA.

With the Show My Work feature, I can enable any question provided by Cengage Learning to have an optional or required explanation submission. In the editing of an assignment, I can enable this feature as shown in the figure to the right.

From the student’s perspective, the Show My Work feature allows the submission of a solution to be automatically graded. It also acts as a section for the student to elaborate their thinking and understanding of the problem solving that went into their submitted solution.

In Enhanced WebAssign, It also acts as a section for the student to elaborate their thinking and understanding of the problem solving that went into their submitted solution.

The fidelity of their mathematical thinking is enhanced with rich-text formatting tools complete with mathematical symbols. In addition, students can upload pictures of their written notes devoted to their problem solving for inclusion in the Show My Work feature. The fidelity of students' mathematical thinking is enhanced with EWA's rich-text formatting tools complete with mathematical symbols.







In my classes, I conduct our mathematical learning sessions in classrooms equipped with enhanced digital capabilities that include the use of a stylus or digital pen with each computer. This affords me the opportunity to use the more integrative Enhanced WebAssign tool known as the PencilPad. We have successfully used PencilPad embedded with a wide variety of questions including: existing publisher questions, separate support questions, to questions with multimedia features like the popular Watch It resources. Student using Enhanced WebAssign's "PencilPad" feature

The immediate advantage of the PencilPad is the integrative nature of the tool with existing questions. The PencilPad tool affords the student a greater level of mathematical and cognitive fidelity in their conveyance of their conceptual understanding of the problem. It is essentially digital paper. Numerals, fractions, symbols, and operators are easily scribed in conjunction with the solution submitted by the student for immediate grading and feedback.

The communication within the PencilPad tool is two-way. Once a student submits their work, teacher formative assessment can be returned to the student that can confirm their conceptual understanding or correct any misconceptions that may be present in the student’s thinking. This is crucial for a student who receives a correct mark for their submission, yet benefitted from fortunate alignments of technique and not a complete understanding of the problem.

Numerals, fractions, symbols, and operators are easily scribed in conjunction with the solution submitted by the student for immediate grading and feedback.

For both tools in Enhanced WebAssign, opportunity to convey partial credit for work that is conceptually sound is available. Keep in mind, this information is digitally compact and stored for each student on each question and assignment creating a portfolio of student learning visible for all to see. As I hope you are thinking, the connections between these two Enhanced WebAssign tools and student learning allows us to uncover and make visible the conceptual understanding of our students’ mathematical problem solving.

The process of peering into a student’s mind and affirming that their understanding is true can now be aided with the Show My Work and PencilPad features of Enhanced WebAssign. Using these tools has helped my students elevate in mathematical achievement, and my hope for you and your students is to experience the same.

Are you an Enhanced WebAssign user? How do its tools help students build and show their understanding? Share your experiences in the comments.

Michael Lafreniere is an associate professor of environmental engineering technology and mathematics at Ohio University-Chillicothe, where he has taught since 1994. He received his B.S. in Electrical Engineering in 1991, and his M.E. in Environmental Engineering in 1994, both from the University of Florida. Currently, he is working on a doctoral degree in mathematics education from Ohio University to improve the science, technology, engineering, and mathematics (STEM) offerings available to students. Mike uses Enhanced WebAssign in conjunction with self-made, online videos and a 1:1 tablet computer environment in what he calls a “Collaboratory.” This includes in-class and online students where students in his STEM courses benefit from the mastery approach inherit with WebAssign’s randomization features. Mike stresses the conceptual understanding, adaptive reasoning, and strategic competencies in conjunction with the procedural fluency commonly found in STEM courses. He provides the support and patience necessary for colleagues to implement many of his experiences in teaching and facilitation of learning.