You are teaching problem sets to a group of 15-20 undergraduate students. They have differing levels of experience - some students excel at mathematical and quantitative skills, but others do not have this training or inclination. This results in a variation in the levels of effort exerted by students and interest in their coursework. Some believe the quantitative approach is ‘bogus’ or have ‘math anxiety’ and find it difficult to engage. Others lack the training but try hard. Students with a greater understanding of quantitative approaches find the classes straightforward, and a little too easy sometimes. How do you engage all students in the classroom?
You lead the class and work through all the questions in the problem sets very slowly, by spelling out the steps for those students who find the problems difficult. All students work individually, and directly engage with you to clear their doubts.
On the positive side, all students will all be on the same page. This may be desirable if learning outcomes are measured using test scores on an exam. On the negative side, quantitative students may find it too boring. Learning is top-down and non-collaborative, as students do not co-produce knowledge. Qualitative students may also feel put on the spot, if you focus on them too much.
You go through the main steps and provide solutions of the most important questions in class. You focus on theory/key concepts and draw out the applicability of the concepts to the real-world using student group discussions.
The dual focus on problems and group discussions, the former for quantitative students and the latter for qualitative students. On the positive side, you include teaching methods familiar to both types of students and involve students more in the learning process. This will improve the attention paid in the classroom, if done thoughtfully. On the negative side, qualitative students may be more engaged in the discussion, and quantitative in the problem sets (and possibly group discussion). This may not result in desired learning outcomes, as students may stick only to what they already know.
You encourage students to work in groups or pairs. You ask students with strong background skills to work with others, who are new to problem sets, with the objective of solving problems together.
You guide the class, and students steer the achievement of class tasks through the problem sets. On the positive side, this encourages peer learning and creates a congenial learning atmosphere, if guided properly. On the negative side, qualitative students may feel insecure, if they cannot reciprocate through teaching their peers. Learning is also subjective, i.e., it depends on peer dynamics within each class, which in turn may vary significantly.
You work through the most important problems in class and encourage discussion/reflection about the relevance of the concepts. You set extra problem sets and 19 practice questions for those who want more practice. There are more difficult problems for who already have training, and easy problems for those who don’t.
Dual focus on problem sets and class discussion, with extra work for students to take home. Positive and negative aspects are comparable to the discussion of point 2. Homework and additional learning maybe useful to those highly motivated students. But those who are math phobic may not benefit, as they may opt to avoid rather than engage.
Consider doing a combination of learning activities, such as leading the first few problems, group work for a few, class discussions, games etc.
How best to leverage peer learning in this environment, by tapping into everyone’s strengths?
Homework/practice questions are more likely to help those who are more motivated, especially because repetition is important to building intuition.
How does one reach less motivated/indifferent students?
Account for pattern of examination testing i.e., do they have only problem sets on the course or essays as well? Can concepts to applied to real world?
Setting expectations early in the course may ease anxiety. It may also reduce effort if problem sets are non-compulsory. How would you reduce this trade-off?
Those who are ‘math phobic’ may require special attention as they may be underconfident in mixed-ability settings, especially if they compare themselves to their peers.
Negative stories/narratives about abilities: students may tell themselves stories about how they are bad at math. Would you challenge them? What tools will you use to gently persuade them to reconsider their self-concept?
There may be information overload, if there are many students without any quantitative background.
Pace of learning in classroom, as well as take-home tasks will matter
Working with a friend maybe helpful, along with more focused attention and follow-up in office hours, additional tutoring from the department etc.
How can learning be two-way, i.e. where both quantitative and qualitative students help each other learn?
References and resources
Beilock, S.L. & Willingham, D.T. (2014) Math Anxiety: Can Teachers Help Students Reduce It? Ask the Cognitive Scientist, American Educator, 38 (2), 28-32.
Benedict, M. E., & Hoag, J. (2002). Who’s Afraid of Their Economics Classes? Why are Students Apprehensive about Introductory Economics Courses? An Empirical Investigation. The American Economist, 46(2), 31–44. https://doi.org/10.1177/056943450204600203
Oswald, D.L. & Harvey, R.D. (2000) Hostile environments, stereotype threat, and math performance among undergraduate women Current Psychology, 19(4), 338–356. https://doi.org/10.1007/s12144-000-1025-5
MacInnes, J. (2016) Statistics Anxiety A Fairy Tale for Our Times? Podcast