# Teaching a new, large topic: present in class or assign as homework first?

In spring 2019, I will be teaching a master's level course in applied statistics for students in economics and management. The main topics are linear regression, explanatory and confirmatory factor analysis and clustering. The course is part of a study programme that is organized in a peculiar way. The classes are lumped together in 2-day or 3-day chunks with 3-week breaks in between. So the schedule is something like this

For k between 1 and 4:

Week k  : independent work, no classes
Week k+1: independent work, no classes
Week k+2: independent work, no classes; mandatory homework to be delivered on Thursday
Week k+3: classes on Monday, Tuesday (if k is even, then also Wednesday)


Each class is 45+45+45 minutes (with two short breaks in between). Since there are four main topics, there probably will be one topic per 4-week cycle with two or three lectures of 45+45+45 minutes. The question is,

Which of the following two approaches to teaching is likely to work better?

Present the theoretical material in class. Show some examples of solving exercises. Give the students some time (perhaps 45+45 minutes) to work on example exercises in class with opportunities to get help.
For the homework assignment, ask them to solve some exercises and answer some key questions about the topic presented in class. Before the next class, post a solution online.
2. "Inverted approach"
As a homework assignment before the class, ask the students to read new material, answer some key questions about the topic and solve some exercises.
In class, present the same material briefly and discuss what they have read and solved. Show some examples of solving exercises. Give the students some time (perhaps 45+45 minutes) to work on example exercises in class with opportunities to get help.

This may sound complicated, but the main difference between the two approaches is when the students encounter new material first and when they independently solve the exercises related to the topic.

1. In the traditional approach, they first learn the new material in class and then practice it independently after the class.
2. In the inverted approach, they learn the new material and practice it independently before the class.

Somewhat related question: "Master's-level Quantitative Methods / Statistics textbook for Management, Marketing, Economics students".

The traditional approach is likely to work better, not because it is particularly brilliant but because the inverted approach is worse.

My main concern with the latter is that students who have rather limited understanding of and skills in statistics (I expect the vast majority of my students to be like that) may not be able to effectively study a large topic (25% of the whole course at once) independently. Reading the textbook unassisted may be overwhelming. They may answer the questions and do the exercises if they are forced to (through mandatory homework) but they may still have a hard time understanding the essence and what they have done in solving the exercises. In fact, they may get so confused by independent study of a large topic that the classroom explanation that follows may not be all that effective in "deconfusing" them.

My second concern is, the students do not get to practice independent problem solving after the class, so they do not get to strengthen their understanding following the class.

The inverted approach is likely to work better because it uses the lecturer's time more productively. The students come prepared and have almost learned the topic by themselves. That allows classroom discussions of the topic on a level that is not achievable unless they study the new topic before the class.

• To be sure this is not a bug, did you make the case for the alternative position in another answer? – Heteroskedastic Jim Dec 3 '18 at 17:22
• @HeteroskedasticJim, I wrote two answers supporting opposite positions. I am hoping to see one getting more upvotes than the other and this way learn what the majority of the people here think. – Richard Hardy Dec 3 '18 at 18:41

The beauty of teaching is that you can use a variety of teaching methods throughout the same course. If you just pick one method and stick with it for the rest of the course, it becomes predictable and loses its effectiveness.

Different students learn the same concept/skill in different ways, which is why it is crucial to switch between methods when teaching.

For example, I am a visual learner and need to see concepts explained with the help of pictures, drawings or diagrams. It is extremely difficult for me to understand a concept which is explained verbally, without the help of any visual aids. My brain eventually tunes the verbal explanation out and starts thinking about something else.

So what I would recommend first and foremost is that you spend your first class getting to know your students: what are they like? how much do they already know? what type of learners are they? how much guidance do they need to learn? etc.

Of course, by the time your first class arrives, the teaching framework will already be in place. But even so, you can have some flexibility around that framework to make sure the course is responsive to the actual needs and strengths of the students.

When I used to teach as a sessional lecturer at the university level, I designed my graduate-level course around the skills I wanted the students to acquire by the end of the course. For example, I wanted them to be able to conduct a data analysis (e.g., multiple linear regression), write a detailed report presenting the results of that analysis and prepare and offer a presentation which highlighted the main findings of the report.

To this end, I would use different techniques to help my students build these skills. In one class, I would have them brainstorm together on the main components of a written report. In another class, I would have them go through a guided multiple linear regression exercise on their laptops. There would also be a class where they would present statistical findings as part of a team in front of the class and the remaining teams would provide feedback and offer suggestions for one thing they could improve on in future presentations, be it slide content or personal presentation style.

This framework, driven by skills rather than concepts, was flexible enough to provide students with the opportunity to do something different in each class. Their constant participation in their own learning was key and that participation could take a series of forms. Of course, there were lectures too, but there was also room for the students to get engaged in class.

The framework is something I developed at the time based on my own experience with university-level courses I had taken as a graduate student. After graduation, I found many of these courses to be unhelpful - they didn't really prepare me for the real world. So, in designing my courses, I wanted my students to acquire practical skills they could put to good use in their professional lives. It is often easier to acquire the skills first and understand the concepts later - many of us who do applied statistical work find themselves in this situation.

If your course involves a big self-study component, it will still be important to provide students with deeper guidance beyond "read article x and read pages 10-90 from book y". Perhaps have them ask a few salient questions based on that reading before they come to class, or give them a heads up on the concepts they should pay attention to, why they are important, how and when they tend to be used in practice, etc. Also, for the same concept, assign readings which come at the concept from different vantage points, or assign both a text and a video explanation, etc. Or ask them to keep track of what aspects of the concept they found easy and what aspects they found challenging, so that you can focus in class primarily on the challenging aspects.

Not everybody is a self-learner - the reading tasks will cater most to self-learners. To this end, you could assign concepts that are easier to comprehend for self-study but cover the more nuanced concepts in class.

Using a variety of approaches is your best bet of leveraging what the students already know and what their strengths are with what your overall goals for this course are. At the end of the course, the students should be able to solve real-world problems applying the concepts and skills they have learned in class (at least in my view). Everything else will flow from this!

• I did not respond to your answer earlier, but at least now let me say thank you (and sorry for the delay). I have a reason to seek a yes/no answer – it can be used as an argument in a discussion. That is why I was not particularly enthusiastic about yours. On the other hand, I do admit that all of your points are relevant and enlightening, and there is no doubt I may benefit from implementing your ideas in my teaching practice. Thank you. – Richard Hardy Dec 13 '18 at 11:18
• @RichardHardy: Thank you, Richard! I guess it's hard to provide a yes/no answer - it really depends on the make up of your class. One class may react better to yes, another may react better to no. The best teaching is adaptive to the actual needs of the students. We can make the best plans at home but when we show up in front of the class we might need to alter them or ditch them altogether if they turn out to be ineffective. The human brain craves variety anyway in a learning context in order to remain engaged in the learning process. You can set up an experiment to test your yes vs no? – Isabella Ghement Dec 13 '18 at 15:28