Dr. Mom, My Adventures as a Mommy-Scientist

Discussion of my journey from grad school to postdoc to tenure with two kids, a husband, (and a bit of breast cancer) in tow.

Monday, March 12, 2007

Teaching to the Top

I am starting to hear feedback about my teaching and have hit an ideological question. Should you teach to the top, middle, or bottom of the class? A student in my class was talking about her struggle to understand the concepts this quarter. She's doing okay, but feels much less certain about the material than she did last quarter. She described what the instructor did last quarter. He had the class work on worksheets, which were shorter versions of HW problems. His exams were very similar to worksheets. I would consider this teaching to the middle. He is teaching students how to perform concepts in exactly the same way that they are presented in the text, but he is not encouraging them to grow beyond the text to to recognize problems in new situations that can be solved with the same tools.

Turns out I have been teaching to the top. I have been really encouraging my students to stretch and reach to that synthesis phase of learning (never thought I'd use that Bloom's taxonomy stuff but there it is). I want my students to understand the material deeply so that they can see how the principles and equations that they learn are applicable to other problems and to daily life.

The problem with teaching to the top is this. Students at the top feel pretty good. It is a little hard, but they get it. This is about the top 15% of the class. The middle students (25-85%) have trouble getting it. They are used to understanding and feeling comfortable with concepts and for what may be the first time thing aren't coming easy to them. Because of this, they lose confidence in their abilities which can negatively impact their grade. I have seen students who are doing well in general make simple mistakes because they don't feel "sure" about a problem. Several studies examining the classroom environment for women and minorities have shown that confidence in one's abilities (perceived or actual) can influence performance. So perhaps teaching to the top undermines the abilities of the middle section of class, which is most students. Meanwhile the bottom part of the class (last 25%) really doesn't get it. If a student would normally have trouble getting a concept as written in the book, they will have a great deal of time stretching that limited understanding to new classes of problems.

So the question is: which is better to teach to the bottom or the middle or the top?... and if I teach to the middle or bottom, how can I be sure that the top students are still challenged? How can I encourage students to develop a synthesis level of understanding without undermining confidence in their abilities.


At 12:21 AM , Blogger lilk79 said...

Hi Dr. Mom,
I'm just started my first blog, so check it out...

The answer to your great question is however... none of the above. I don't truly know how much formal "Teaching" training PhD/professors have, but the ideal teaching situation is to differentiate your class/material. This can be as simple as giving multiple types of assignments to assess the same goal, or it could be a modified assignment for students who are struggling. I teach middle school mathematics, and while I do tend to "teach to the middle" I am fortunate to have a handle of the students who need extra support and can work with them in small groups, especially when a difficult topic is approaching. The same is true with my advanced class-- I don't give more work, but more challenging work dealing with the same material.

A specific example would be with algebra. My struggling students might be working in partners to solve five equations, while my middle of the road students might have five more challenging equations, or might need to work independently, and lastly my higher achieving students may have to create equations from story problems or create a real life model for the equations.

Long story short-- you should be teaching as many different approaches and planning for multiple learning styles and abilities, and not just teaching to one group.

At 3:29 AM , Anonymous Anonymous said...


I'm writing to agree with the above response. As a teacher I am expected to teach for the individual needs of my 32 students. This includes providing extension opportunities for those of higher ability and support for students who are sruggling.

One of the easiest ways of ensuring that you achieve this is to group your students according to ability.

At 10:42 AM , Anonymous Anonymous said...

I also agree with the first 2 posters here. Sometimes as teachers we have to step back and ask ourselves, what do we want everyone to take from this class? While we know there'll be some students on the fringes, top and bottom, there should generally be a way to present the material and structure assignments if not always exams to provide material that can challenge everyone.

I think, and I've had this conversation with both younger and older professors and all levels but more recently some younger math professors, is that we sometimes can get caught up in the good feelings that we feed from when we teach and are rewarded by progress of good, bright students learning from what we present. It's not a secret that it's somewhat pleasant to teach students that are intelligent, eager to learn, who come prepared and have good questions. It's more work to raise a C or D student to a B or C than it is to raise a B student to an A.

At 11:44 AM , Anonymous PA said...

I am not sure I agree with the other commenters who seem to mostly be speaking based on experience at levels below the university level. When someone is accepted to a university, it is with the understanding that the admissions people believe that the student will get a degree from that university. Simply, there is only the expectation that most students will PASS. There is no assurance that every student will or should get high grades. A university setting is supposed to teach students to think critically. It is not, as in the case of lower education, required by the state, meaning that it is extra education that the student pursues to reach a higher level of knowledge.

I would say, teach to the upper middle, provide plenty of outside resources and reading for the top students, and be available for those that struggle. If some students at the very bottom just can't catch on, they can take the class again, take another, or choose to transfer to another university. Universityies are places of higher learning and that is what a teacher should be pressing, not making each and every student feel confident or happy. Welcome to life, kids, sometimes its hard.

Also, I must congratulate you on pressing the students to reach. The professors that most challenged me, those that most of the other students disliked, were those that I most admired and learned from.

At 1:32 PM , Blogger lilk79 said...

My main concern about what PA has said-- is that your job is still to EDUCATE students. I'm thinking of a specific case, but I think the same philosophy should follow no matter what level of education. If students are being required to take certain courses, especially those not in their areas of strength-- I think it is a professor's obligation and duty to provide the most support possible. This might be tutoring, office hours, or with graduate students... and hopefully some of the intervention is happening within the course itself.

A particular situation is my family member who is very challenged with mathematics, but her focus is literature. She is being required to take a math class, and doing everything possible on her own to pass this required class, even though she has no intention of EVER taking additional classes in the field.

I would hope all educators have similar goals to educate, challenge, AND support?

At 2:10 PM , Blogger PhD Mom said...

I really appreciate your comments!In reply to lilk79, I am in engineering so we really only teach classes to majors.

I appreciate yours and anonymous' suggestions to give different assignments according to ability, but am not sure how to make that work in a college setting. Grades need to be fair, so it doesn't seem right to require one set of students to do more work or to do the work differently (i.e., in groups) versus another set of students.

This time I think concepts were mostly taught at the highest level, which left the middle and bottom students behind. One problem was that they didn't know that I was teaching to a high level, and therefore assumed their failure resulted from a fundamental inability to grasp the material rather than an inability to adapt material to new situations. I would like to continue to challenge students, but also provide avenues to apply the material in normal "by the book" situations so that students can gain confidence before applying in a new way. Just not sure how to do this...

At 11:49 AM , Anonymous Anonymous said...

I think PA is not incorrect, but there is also an assumption that all universities have the same goals for their students (which is not true, public universities have different defined goals overall than do small liberal arts colleges than do private colleges and engineering colleges and engineering schools within all of these frameworks fit in someplace in the spectrum). Within this as well, all classes have a general goal as well: a survey type class is not going to have the same basic goals defined by the curriculum chair (and depending on where you are, those people have more and more sway) than the smaller and more upper level classes where, as Dr Mom has said now more specifically, she has specifically all majors and perhaps some fewer students as well. My strategy is naturally different for 20 students than it must be for 120.

At 11:20 PM , Anonymous Flicka Mawa said...

I was reading some of your archives, and I wanted to comment on this. I am one of those students who would have been affected by your class by feeling insecure and progressively getting worse and less confident. I kind of think the first few posts are unrealistic/inapplicable for an engineering course in a required subject for majors. And I think it's great that you challenge the top of the class. In my first classes for the core of my major, I was about average. For me and probably many of the students in your class, these classes represented a big transition (which I wrote about on the post: University and Depression: Part I, the Undergrad years). I didn't have a problem so much with material being hard as I did with realizing that I wasn't dumb for struggling with it.

I have two major suggestions for you:
1)On homeworks and exams, include material that the average student can handle and material that only the advanced students will get. This way the advanced students will feel challenged by the advanced questions and get appropriate credit for it, but the average students will not feel stupid because they got only 30% of the answers. I don't know what kind of means you average, but before I hit my core courses I could handle about 60% as the means. When the mean on a test drops below 50%, even if it's just because the test was really hard, it is very bad for the self esteem of the students and it will be hard for the average student to not feel dumb.
2) When things like a mean of 30% do happen, apologize and tell the class you didn't mean to make the test so hard. Make it clear that it was a test meant to challenge the top members of the class, and that the students are performing extremely poorly despite the low mean on the exam. My #2 is basically that in general, you can make it hard, but be supportive, and TELL THEM that you are making it hard. Be honest that you expect a lot and that those who aren't getting top grades are still good enough to get jobs in the field as long as they push through it, and then be there through office hours, etc, to help them make it through.

At 11:22 PM , Anonymous Flicka Mawa said...

In #2, I meant to say: the students are NOT performing extremely poorly despite the low mean on the exam.

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