# Teaching Initiatives

The Lecturers in the SFU Department of Mathematics are committed to improve student success and make Mathematics more accessible to students of all backgrounds. Some of our initiatives are listed below

#### Diagnostic Test:

The Diagnostic Test is a test given during the first week of classes to all students taking a differential calculus course at Simon Fraser University. The test consists of 30 multiple-choice questions, it is written in the lecture hall, and it is 40 minutes in duration. Distracters among the multiple choices for each question were developed using errors actually made by previous pre-calculus students.

The Diagnostic Test is designed to assess students' knowledge of pre-calculus topics that are covered in Principles of Math 11 and 12. Its main purpose is to be an early warning sign for those students with a weak mathematical background. On the Diagnostic Test students receive a pass/fail marks. The passing score is usually 18/30 and higher. As an incentive, students who pass the test automatically receive 5% of their final mark for the course. Students who fail the test are advised to attend Calculus Support Sessions. Through regular attendance and online-based homework each student who failed the test may recover the portion of the course mark that is attached to the Diagnostic Test.

Students with low marks on the Diagnostic Test are advised to take a pre-calculus course offered by the Department of Mathematics.

There is evidence that student's result on the Diagnostic Test, specially when combined with high school math grades, may be a good predictor for student's success in Calculus.

For more information about the SFU Diagnostic Test contact Justin Gray at jgray@sfu.ca or Brenda Davison at bdavison@sfu.ca.

#### Homework Quizzes:

Due to the large size of entry level math classes at Simon Fraser University and the limited number of teaching assistants’ hours, traditionally only one or two questions per weekly paper assignment were thoroughly marked. It was noticed that marks on paper assignments were generally very high and that they did not correlate with final course grades. In addition, it was noticed that solutions to all posted homework problems were easily available to students at any time. In an attempt to address our concerns about the purpose of homework assignments, in 2009 weekly in-class homework quizzes were introduced.

Each homework quiz consists of two questions, is about 10 minutes in duration, and it is written at the end of class. To succeed in for the homework quiz students need to understand the content of the weekly homework assignments. Each week an assignment is posted in the WebCT course container. Assignments consist of Instructor's Questions and of questions from the textbook. These assignments are designed to encourage students to practice throughout the semester and are essential in developing understanding of course material. Assignments are not to be handed in. Instead, questions on the weekly homework quiz are taken straight from the corresponding assignment. The fact that each student writes the homework quiz by herself in settings similar to those of midterm and final exams, i.e., in a lecture hall environment with a time constraint, provides an opportunity for students to assess their own progress in the course more realistically.

It has been noticed that the general trend of scores on homework quizzes matches the trend of the total course marks.

For more information about Homework Quizzes contact Justin Gray at jgray@sfu.ca or Jamie Mulholland atj_mulholland@sfu.ca.

#### Journal Approach To Learning:

The concept of a **homework journal** is introduced to help students to organize the course material and to be actively and reflectively engaged in their own learning. Each summative assessment such as assignments, quizzes, exams, etc. comes with a rubric similar to the following: done, checked, corrected, studied for midterm exam, and studied for final. These rubrics are meant as a guide for students to stay on top of their studies.

Students are advised that their solutions must be neatly presented: question should be well spaced, no scribbles or items scratched out, explanations should be written in full sentences, all writing should be clearly legible, etc. The detailed guidelines are posted in the course WebCT container.

When meeting with the instructor students are expected to bring this homework journal. A student’s homework journal gives an opportunity to the instructor to look at her or his progress through the course, understanding of the material and ability to write clear solutions. Hence students get personal one-on-one feedbacks on their ability to write clear and well presented solutions.

Below are samples of suggestions to students for using their homework journal:

- Do rough work on scrap paper. Once you have a clear idea of the solution then write the final version in your journal.
- Multiple solutions to assignment questions are encouraged. One of the most important, yet neglected, parts of problem solving is reflecting on your solution. When you find a solution, try to see it as a whole without all the little details. Also, try to discover a different solution, perhaps a more efficient solution. This will benefit your quiz and exam writing ability.
- Do questions in order. Clearly label question and section numbers so you can find them easily when it is time to review.
- Grade your own assignments once the solutions are posted. It is important to find any mistakes you have made since this is a valuable learning opportunity. Many uncaught mistakes you make on the assignments will prove costly on exams. So why not catch them now and learn from them when the stakes are low.

For more information about Journal Approach To Learning contact Petra Menz at pmenz@sfu.ca or Jamie Mulholland at j_mulholland@sfu.ca.

#### Online Assignments:

The three facts of 1) practically giving no feedback to students on their paper assignments, 2) not ensuring that the students practice concepts and skills sufficiently, and 3) the high costs of marking paper assignments were the main reasons that the Department of Mathematics at SFU decided to introduce online assignments for its science/engineering calculus course sequence in the summer semester 2003. SFU subsequently adopted online assignments for the social science calculus course sequence in the fall semester 2004.

In our experience the most valuable feature of online assignments is that this medium allows the instructor to reach each student in the class at her will. For example, an online assignment that is due before the *second *lecture in the semester makes students do the coursework from day *one*. In our classes, we use short multiple online assignments that are often closely related to class lectures and definitions, theorems, and examples from the textbook. Many of these problems are phrased as multiple choice, true or false, and matching questions, rather than in the back-of-the-chapter-exercise fashion. Assignments are due before the next lecture and, hence, students have to go through the course material after the lecture in which the material is covered. In a survey that was conducted in a Calculus I class, students were asked to respond to the statement, ”To complete online assignments I had to read the textbook and lecture notes regularly.” The summary of 230 answers shows that 83% students agreed or strongly agreed with the statement.

We also use online assignments as a drillmaster. For example, as an assignment question we post a dozen limits divided in groups of three with one submission per group. We anticipate mistakes that students might make and we create hints accordingly. Multiple tries are allowed.

For more details about Online Assignment contact Veselin Jungic at vjungic@sfu.ca or Petra Menz at pmenz@sfu.ca or click here.

#### Online Calculus Course:

Online Calculus Course: An online version of a differential calculus course has been created in an attempt to answer the question: What should be done so that a calculus course offered online provides students with an experience as close as possible to the live classroom?

In their attempt to answer this question, the course authors were led by the following principle: provide the student taking our distance education course with an experience as close as possible to the live classroom. Thus our online course has the same structure as the live course and uses the same material: the same class notes are used in lectures, the same online assignments and the same concept of paper assignments is used to check students’ weekly progress. The two midterms and the final exam are created from the same already existing repository of exam questions. The main and obvious difference is that we deliver content of our lectures via video lectures. Our videos feature two windows on the same screen: one window is used to show the recording of the instructor's image and the other window serves as a notepad for the instructor’s writing or as a screen for various demonstrations. Students are directed to download a skeleton outline of the notes and follow along with the video lecture to fill in the details. Having the instructor's face (and upper body) in the video means we don't have to constantly be writing; we can underline what we are saying by using body language, waving our arms around, making gestures and facial expressions, for example, much like we do in class. Also within this video we include animations and applets that have been created over the last few years to help students build their conceptual understanding of the material. All this is synchronized with the audio and video recordings of the instructor’s comments and explanations.

For more details about our Online Calculus Course contact Veselin Jungic at vjungic@sfu.ca or Jamie Mulholland at j_mulholland@sfu.ca. For a few promotional videos click here.

#### Calculus Support Sessions

Students who fail the Diagnostic Test are strongly advised to attend the Calculus Support Sessions (CSS). CSS is designed as a 10-week (1 hour/week) program covering various topics in pre-calculus in small class settings. The sessions are open to all students registered in differential calculus courses, regardless of their score on the Diagnostic Test. As an incentive, students who failed the Diagnostic Test are assigned 3% of the course mark for their regular attendance and active participation in the Calculus Support Sessions and 2% for correctly solvingadditional questions posted online.

For more information about the Calculus Support Sessions contact Brenda Davison at bdavison@sfu.ca.