Talk:University of Arizona Task Force on Core Mathematics

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Entry Level Courses

i propose to move this to the discussion area and bring it back if appropriate [uribe 4/5/06]

Is it possible to consider making all first courses (Math110, Math 124, etc.) 3-units? (This question from Jeff Golderberg, I think. [No, it was from Uribe] What is the reason for wanting this?Wgmccallum 11:31, 22 March 2006 (EST)) Besides being extremely costly to many students (in terms of risk), if all these classes were 3 units, we would have some savings in resources which could get re-used, perhaps by opening more sections.[uribe 3/29/06] There is a 3-unit version of Math 125, it's Math 125. This course would be a disaster for most Math 124 students. If we want courses to be 3 units, we need to rework the curriculum. In particular, we'd have to replace the 124/129/223 sequence, which in totality has 12 units, with 4 courses. This might solve the problem of students risking too much on a high unit course, but it wouldn't have the savings in resources. 63.227.83.155 10:56, 31 March 2006 (EST)

A suggestion was made Friday to enable a way to identify struggling students early on, so that corrective measures or more adequate advising be provided to students before they fail the course completely. SuccessNet could be that tool, although collaboration with colleges and departments would be needed to customize communications.[uribe]

Side Discussion on entry level teaching quality

I propose to move this discussion to the "discussion" page and bring it back when Resorces are discussed. [uribe, 4/5/06]

I got an earful about Math teaching the other day. In an early meeting of this group, Joaquin stressed the point that most of the times, the complaints he hears are about Math teaching. This advisor said one of his students' math instructor has very poor teaching skills: talks to the board all the time; has a strong accent; when asked a question, he/she repeats what has been written on the board (the cause of the confusion, I suppose) or says "you should know that" and goes on, etc. This advisor raised the issue when a math advisor came to his college to explain Math placement. Apparently the math advisor just shrugged and said "well, that is the way it is" and dismissed the advisor (I don't believe it was quite this dry, but ...) I believe we must recommend strengthening our porgrams to develop our graduates as effective instructors. I defend the TA's almost all the time ( I was one, how can I forget!) but recognize that the training is scarse and many of the grads may see themselves a "research mathematicians" and may undervalue their development as future Math instructors. We have to make teaching a fornmal component of our programs of study. [uribe 3/29/06]

I think it is unfair to judge all TA's on one anecdotal account. It is also clear that we are more likely to hear reports of problematic teaching, even if these are isolated events. I believe almost all of our TA's get good teaching evaluations, and they have to take a teaching training course before they are put in charge of a class. I think we can check TCE records to get supporting data, but I've always thought that the average rating of teacher's effectiveness in the Math Department is 4 (out of 5), which I think is exemplary given the number of instructors we have in the Department. Bill, am I correct? JLega 15:34, 30 March 2006 (EST)

I know this better than many - I was one of "those international TA's" whose accent "was the problem". I am surprised that you took this as judgement. This anecdote is not isolated; comments like this one are more the norm than the exception. I get to hear them daily from students and staff alike. You could too; just step out of teaching mode for a day or two.

Unfortunately, comments like this are consistent with Joaquin's desire to investigate the quality of teaching in Mathematics. Keep in mind that the Dean's wants to provide "quality service" to the community; and quality is usually measured subjectively through the client.

Even if the students rate teaching well in the evaluation and "use this issue" to justify their shortcomings, it is in our best interest to produce a visible development program so that these criticisms, real or imagined, don't have any basis at all. Besides, I believe one can never have enough quality.[uribe, 3/30/06]

It seems to me this discussion belongs with the other subcommittee, so I'm taking the liberty of moving it to a separate subheading. However, I have two things to add: a) I'd like to see some actual numbers here, and in particular I'd like to know what proportion of complaints are about the math department. Then I'd like to compare that proportion with the proportion of entry level SCH taught by the math department. b) We do have in place extensive TA training: they take a one week orientation, a one credit, 2-semester course, and they all have supervisors who visit their classes twice a semester. And we have an internal evaluation system that removes particularly bad instructors from teaching.

Quality of math instruction is always going to be an issue for many people. Lots of people who take a required math course needing to meet an inflated grade requirement are going to have a disappointing experience. Complaints are part of life in Math instruction with well over 100 instructors.

We take complaints seriously anyway. Math does intervene in classes where the level of instruction is below the norm. At one time in the recent past, we could and did take action to help an instructor who needed it more quickly. But as we have been pushed further and further to the wall, this has become more difficult. Still "Well that is how it is" isn't the department's stand.

To act on a complaint, we need to receive a complaint from a student. It is unfair to an instructor to go to them with anonymous and second hand complaints. If, for other reasons, we suspect there might really be a problem, we will follow up on such complaints, but normally we cannot. You would be surprised how often we receive complaints about a “Math TA” that are neither TA’s nor in Math.

Math requires a great deal of training before its GTA are put in the classroom. It hires the best adjunct faculty available. It monitors the teaching of its regular faculty, and make it as important a part of promotion as research. Quality matters! --D Madden 15:53, 1 April 2006 (EST)

I agree totally with Dan's points. My suggestion is not to act on anonymous complaints; instead, I suggest to strengthen our efforts to increase quality teaching, to make teaching skill development an integral part of the training our gards receive and to make it an integral part of this plan. By doing this, at least, we will be giving pre-emptuive strikes to anonymous complainer.[uribe 4/7/06]

It occurred to me that we need to include a deliberate plan to communicate with the community on the efforts we make continuously to improve the quality of our services. In a separate discussion I heard that efforts to maintain links with our constituents are "not often cited as an important part of the Department's mission. And therefore continued funding support for this effort is difficult to maintain." Oftentimes perception is everything; and if we are perceived as poor performers, no matter what we do, we will continue to be perceived as that, particularly if that places the blame for failure conveniently on us. Like it or not, we need to fight this misperception. We need to publicize our leadership in teaching and learning, our high marks in course evaluations, etc. especially to those who like to generalize out of one anecdote. [uribe 4/13/06]

Text taken from Quality Instruction

It also needs to be recognized that Mathematics will always be forced to compromise between quality and quantity. [I belive this line of thought is in part what has provoked many of the problems we are facing. I submit that the department should focus on quality. If quantity is insufficient, then we have to go get more resources. In the current environment, if we keep doing more with less, we will continue to see our resources reduced --150.135.169.243 15:52, 12 May 2006 (EDT)]

However, the first responsibility the Department will usually have is to assure that every student will find an instructor. --150.135.169.243 17:11, 12 May 2006 (EDT)

It takes time for the Department to sort new people into these categories and assign them appropriately. Still the current reality is that the Department sees between 20 and 40 instructors new to the University each year. This is why the risk in assigning instructors will always be unavoidable.

This risk can be reduced mostly by returning to a position where Math resources are far less strained. --150.135.169.243 19:00, 12 May 2006 (EDT)

Text Taken from Resources

Could recommend something. If we are going to make recommendations on this we should know the answer. Problem is that tuition is too low. Maybe impose a tax on taking a course more than 2 times.

The department is chafing at the bit to get involved in new intitiatives like the biology course. The faculty recognizes that the only way to do this is to cut back on something else, but we can't cut anything else. We really are at a crisis point.

Text taken from Technology

Comments from Joceline:

• Regarding technology standards, it is often difficult to make recommendations because many people tend to use their favorite softwares and may not necessarily welcome recommendations to use different packages. This being said, if we decide to make recommendations, I think MATLAB is a wonderful package. It has the following advantages (in no particular order):
  • We can get classroom licenses for a nominal price (2 years ago, it was less than $50 per workstation for a perpetual license).
  • If we want to always use the latest version, it is possible to purchase maintenance licenses. Currently, The MathWorks issues 2 updates per year.
  • The basics are easy to learn.
  • It is becoming a standard, and knowledge of MATLAB is a skill that students can put on their CV's.
  • In our discussions with ARL researchers, one suggestion we received was that Math should teach a course on MATLAB for graduate students in the life sciences.
  • The Information Commons as well as the engineering labs have MATLAB licenses on their machines. Students can thus go there to complete MATLAB-based homework assignments.

I currently use MATLAB in my Math Modeling class and this works extremely well.

I also think we should consider online grading, my preference going to Maple TA, which would allow instructors to create their own questions. I believe LTC is willing to look into this. As far as classroom technology is concerned, I think it would be nice to have instructor computers and video projectors in each of the classrooms where we teach, with a simple way for us (the instructors) to upload the material we plan to use in class on these computers (by that, I mean we should be able to remotely connect to a classroom server from our offices). I think we should promote the use of clickers (i.e. automated response devices). Students would have to buy clickers only once and would be able to use the same device in all of their courses. This year, LTC is running a pilot study with one response system. My understanding is that if all goes well, then it could be adopted as soon as next fall.

Jeff: It would be nice if people could use Excel as well.

Comments from Dave G: The following are some random thoughts. There are a couple of things that need to be kept in mind when using technology in the classroom. One is that the course is not about using the technology but about the content of the course and must be handled as such. However, there will be many students with little or no experience with the programs in question (Matlab, Excel, etc) and there is the question of how to deal with the problem of "getting over the hump" with the program, i.e., learning enough about the program to do the assignments. I think many math professors do not want to have their office hours become tech support for Matlab, and it can remove focus from the mathematics itself if not done properly. In some disciplines, there is an extra laboratory section which deals with this problem, but would require more resources obviously. Also, some course might have less of a definite program that is used but only requires knowledge of _some_ program from a list (much like how we allow different calculators now). When I was an upper level computer science major, many courses required programming but did not specify the computer language you use (C, Pascal, Fortran, etc). This, however, requires some sort of prerequisite of computer proficiency for the course.

Several thoughts around technology [uribe 4/5/06] Questions that should be addressed, for every subject (or client college/department) What needs to be used and why? How much use this technology, and the associated math, is used in the field? What level of skill is expected of the students?

Consider the possibility of online certification of proficiency with some of these packages.

Two types of technology use: illustrative purposes or solving problems.

To some extent, the use of technology can be blended into the mathematics we teach, but we cannot count on adding all technology students must need without adding instruction time or cutting mathematics. Much of the objection to math "technology" in the past is that students do not learn things that once were considered "basic." One might well ask if the ever did, but the real question is whether instructors have stopped trying to teach "basics" in favor of "technology". The above is peppered with quotes because many of the words in this debate have religious overtones in the math ed community. We need to try to stay above this. But we must address the fact that introducing 21st century math enabling technology into a mid 20-th century expected curriculum in a 2006 funding environment requires compromise. The agreeing on amount of compromise and building the consensus to accept it require a large amount of work and a certain amount of time.

The recommendation in our final report can hope for this, but we cannot recommend changes that require it.

By "technology", I meant the use of simulations to better understand or visualize mathematical concepts, not as a way to replace basic mathematical techniques. In particular, I do not think it would be a good idea to teach students how to use say Maple as a replacement for teaching them algebra. On the other hand, we can use technology to help students visualize flows of differential equations, visualize vector fields and surfaces in three dimensions, iterate linear maps, etc. The list is potentially endless. JLega 20:36, 11 May 2006 (EDT)

Resources for instructional design

A fairly large list of Constructivist Instructional Design Models is available from Prof. Martin Ryder’s website at the University of Colorado-Denver at

http://carbon.cudenver.edu/~mryder/itc_data/idmodels.html#constructivism

This bibliography could provide starting points in the improvement of our curricula and lesson plans.

The Committee on Undergraduate Programs in Mathematics (CUPM) of the Mathematics Association of America (MAA) has proposed a set of recommendations to implement or improve Mathematics Programs in Colleges and Universities: (Check entire document at http://www.maa.org/cupm/curr_guide.html)

Recommendation 1: Mathematical sciences departments should

• Understand the strengths, weaknesses, career plans, fields of study, and aspirations of the students enrolled in mathematics courses;
• Determine the extent to which the goals of courses and programs offered are aligned with the needs of students as well as the extent to which these goals are achieved;
• Continually strengthen courses and programs to better align with student needs, and assess the effectiveness of such efforts.

Recommendation 2: Every course should incorporate activities that will help all students progress in developing analytical, critical reasoning, problem-solving, and communication skills and acquiring mathematical habits of mind. More specifically, these activities should be designed to advance and measure students’ progress in learning to

• State problems carefully, modify problems when necessary to make them tractable, articulate assumptions, appreciate the value of precise definition, reason logically to conclusions, and interpret results intelligently;
• Approach problem solving with a willingness to try multiple approaches, persist in the face of difficulties, assess the correctness of solutions, explore examples, pose questions, and devise and test conjectures;
• Read mathematics with understanding and communicate mathematical ideas with clarity and coherence through writing and speaking.

Recommendation 3: Every course should strive to

• Present key ideas and concepts from a variety of perspectives;
• Employ a broad range of examples and applications
• Promote awareness of connections to other subjects (both in and out of the mathematical sciences) strengthen each student’s ability to apply the course material to these subjects;
• Introduce contemporary topics from the mathematical sciences and their applications, and enhance student perceptions of the vitality and importance of mathematics in the modern world.

Recommendation 4: Mathematical sciences departments should encourage and support faculty collaboration with colleagues from other departments to modify and develop mathematics courses, create joint or cooperative majors, devise undergraduate research projects, and possibly team-teach courses or units within courses.

Recommendation 5: At every level of the curriculum, some courses should incorporate activities that will help all students progress in learning to use technology

• Appropriately and effectively as a tool for solving problems;
• As an aid to understanding mathematical ideas.

Recommendation 6: Mathematical sciences departments and institutional administrators should encourage, support and reward faculty efforts to improve the efficacy of teaching and strengthen curricula.

Although these recommendations do not provide a blueprint for implementation of improvement, they do offer a nice checklist of key ideas to keep in mind through out the design process. It is worth noting that This Task Force has arrived at similar conclusions in some areas – for instance, collaboration with faculty from other disciplines, judicious use of technology, etc.

New Topic; Departmental priorities

At the last writing meeting, the issue of what the Math Department would like to do about the issues brought up in the task force. I cannot speak for the Department, but that will not stop me from trying.

First and foremost, the Mathematics Department wants to train the next generation of mathematicians, research mathematicians and practitioners. But I will leave this description to others.

In its important role as a service department, Mathematics would like to provide the best possible mathematics instruction to every student at the University of Arizona who takes a Mathematics course. It would like to develop well structured and carefully designed courses that provide all the mathematics that a student would need to complete their academic goals. The Department would like to be an active participant in every new university effort that has a mathematical component. They department would like to decrease its current role as a unmotivated entrance requirement to various university programs.

Thus the Mathematics Department would like to work with other Departments and Colleges to design courses that cover the specific mathematical material that their students will need, and will use, in their further studies. The Department would like to see the University restrict the use of Mathematics prerequisites to courses where the course material has direct application and is a graded part of the course. Departments, colleges and degree programs should be discouraged from using mathematics simply as an enrollment management tool.

The Department would like to help develop academic programs timed so that students have the preparation they need when mathematics appears in their coursework. The University should encourage, or even force, the Mathematics Department and other Departments to work toward true articulation of their academic programs. Course sequences including prerequisites should be structured to provide a coherent program of study that accurately reflects the real ability of University of Arizona students. They should avoid setting program timing based on artificial advanced standing or academic progress goals. Mathematics needs to work with other programs setting semester to semester degree programs that give students the time they actually need to complete prerequisite courses before they need them.

The University should seriously reconsider its General Education Graduation requirements. There is no question that every student should graduate from the University with a working knowledge of everyday mathematics. However, the reality of the situation in Arizona is that requiring this is very expensive. It is less expensive per student than providing quality instruction at a higher level, but if a choice must be made, general education must be given lower priority. The University should consider setting General Education requirements that allow the Mathematics Department to focus on providing mathematical skills to students who will need and use those skills before they complete their undergraduate education. The University should develop advising and admissions strategies that force students to make realistic choices about their mathematics courses based on their preparation. Mathematics intensive majors and programs should publish degree programs that allow a student with mathematics deficiencies to plan and complete the full program in a timely manner. Entering students should be asked to make their choice of degree programs so that it accurately reflects their preparation in mathematics or to take the time necessary strengthen their mathematics skills to the required level for the field of study they prefer.

The Mathematics Department would like to limit enrollment in its courses to students who have a reasonable chance of completing the course successfully. The Department should develop objective criteria for measuring preparedness of incoming and continuing students based on sound and defensible data. The University and all its units should fully support the Department�s decisions in the matters. However, the University should offer its students opportunities to remediate their problems through programs that are fully integrated into the University�s academic program and are not punitive.