The typical undergraduate programme is delivered through lectures supported by tutorial workshops. Whilst lectures facilitate rapid coverage of course material, tutorial workshops offer a more personalised, supportive environment within which students can acquire mastery of lecture material through problem solving. According to Lepper and Woolverton (2002), one-on-one tutoring is the most effective method of teaching. However, in today’s undergraduate teaching environment characterised by high student numbers, one-on-one tutoring is very expensive to implement. Instead, tutoring is now often conducted through workshop sessions comprising small group collaborative learning under a tutor’s guidance.
Lepper and Woolverton (2002) compared and contrasted tutoring sessions conducted by highly effective elementary maths tutors, and those conducted by less experienced or by equally experienced but less successful tutors. On the basis of this study, they identified the characteristics, goals, strategies and techniques that contribute to success as an individual tutor. Wood and Tanner (2012)studied these findings, and concluded that they could improve the effectiveness of large class lectures.
Treisman (1992) experimented with collaborative learning in undergraduate mathematics and found that it significantly improved student performance, including those students from historically underperforming backgrounds. Smith (1996) carried out a more formal study of collaborative and cooperative learning approaches and came up with five key elements that ensure the effectiveness of these two learning approaches. Using concepts drawn from Treisman and other researchers, Kasturiarachi (1997) developed a successful workshop model for undergraduate mathematics.
In this blog, I combine findings from these research studies on tutorial practice and collaborative learning to come up with suggestions for running effective tutorial workshops for undergraduate Engineering Mathematics.
Preparing for the Workshop Session
- Be thoroughly familiar with the subject content of the workshop problem sheet.
- Adequately arm yourself with a variety of real-world engineering examples that will help students to understand and appreciate the mathematical concepts covered in the workshop.
- Anticipate the sorts of problems that are likely to appear difficult to students, and those that are likely to be easy.
- Anticipate the likely errors that students are likely to make for each problem question, and prepare prompting questions to enable students to direct themselves out of these errors.
Designing the Workshop Exercises
- Ensure that the worksheet covers all the materials delivered in the associated lecture.
- List the key mathematical concepts to be covered in the workshop at the beginning of the worksheet. Then follow this up with the workshop exercises.
- Order the workshop exercises in order of increasing difficulty and complexity. Ideally, group the workshop exercises into distinct problem sets.
- Start the worksheet with routine problems aimed at reinforcing basic concepts, and end with relatively challenging, open-ended mathematical modelling problems designed to stretch and motivate able students.
- Provide a solution set for the worksheet.
- Ensure that the worksheet fits into the workshop time duration, and have its difficulty and accuracy validated by an external party.
Conducting the Workshop
- Plan your workshop sessions to ensure that they all have the same consistent structure. This allows students to internalise the workshop structure, thereby helping to ensure that subsequent workshop sessions run smoothly with minimal tutor guidance.
- Start the workshop by dividing students into small workgroups and giving them a brief introduction to the worksheet.
- Ensure that each student workgroup works steadily through the worksheet, starting with the easier questions at the start of the worksheet.
- During the workshop move continuously through the student workgroups, providing support as necessary.
- Ensure that each workgroup progresses from one problem set to the next only after demonstrating competence and confidence in the preceeding problem set.
- At the end of the workshop session, issue every student with a copy of the workshop solutions.
Teaching for Understanding
- Establish a personal rapport between yourself and the students. Let the students see you as a supportive, nurturing and approachable individual.
- Be continuously attentive to the students, empathise with their difficulties, and show that you have confidence in the students’ ability to succeed at the individual tasks.
- Constantly use questions, as opposed to giving directions and assertions, to prompt students to discover for themselves what they need to do in order to successfully solve the problems they are working on.
- Avoid giving direct answers to students. Instead, offer hints and suggestions to help students to take the next step on their own.
- When students make mistakes, pose questions that prompt the students to retrace their steps and identify their errors.
- Promote student understanding by consistently asking the students to articulate what they are learning, to explain their reasoning and their answers, and to generalise or relate workshop problem questions to engineering contexts and situations.
Fostering Collaborative Working within Workgroups
- Ensure that students interact to help each other to solve the problem sheet.
- Ask students to explain orally to each other how to solve problems
- Ask students to discuss with each other the nature of the concepts and strategies being learned
- Let students teach each other and explain to each other the underlying concepts behind the problem sets.
- Encourage students to help, encourage and support each other’s efforts to learn.
- Randomly call on individual students to explain their group’s choices, decisions, problem-solving strategies and efforts. This helps to ensure that no student hitchhikes on the work of others.
Kasturiarachi, A. Bathi. 1997. “Promoting Excellence In Undergraduate Mathematics Through Workshops Based On Collaborative Learning.” PRIMUS no. 7 (2):147-163. doi: 10.1080/10511979708965856.
Lepper, Mark R., and Maria Woolverton. 2002. “Chapter 7 – The Wisdom of Practice: Lessons Learned from the Study of Highly Effective Tutors.” In Improving Academic Achievement, edited by Joshua Aronson, 135-158. San Diego: Academic Press.
Smith, Karl A. 1996. “Cooperative learning: Making “groupwork” work.” New directions for teaching and learning no. 1996 (67):71-82.
Treisman, Uri. 1992. “Studying students studying calculus: A look at the lives of minority mathematics students in college.” College Mathematics Journal:362-372.
Wood, William B, and Kimberly D Tanner. 2012. “The role of the lecturer as tutor: doing what effective tutors do in a large lecture class.” CBE-Life Sciences Education no. 11 (1):3-9.