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Re: Motivating grad students to teach thinking inMath simply

by Eldon McMurray

Look at them as superordinate categories. As you look at conjecturing ask where would it fit? Under WHAT IF? with estimating. Defining fits undetr the WHAT category. What is this? Generalizing would fit under WHY? Exploring is definately a WHAT IF? Properties are a WHAT, but they also explain some WHYs? The proposed reasoning approach takes students with little or no math schema to a place where they can at least start a problem. See if you can apply the system in you instruction first then see how the students respond. The first thing our instructors noticed was they spent most of the time writing out HOW and explained WHY orally. Eldon L. McMurray Director Faculty Center for Teaching Excellence Assistant Professor College Success & Academic Literacy Utah Valley State College 800 West University Parkway Orem, UT 84058 (801) 863-8550 >>> sandowda(a)msu.edu 03/08/05 6:43 PM >>> Dr. McMurray, I agree that the three things you list are useful in solving math problems whose solution methods are already known; however, I wouldn't say they're sufficient for "fully understand[ing] mathematics." How do you address central mathematical practices like conjecturing, defining, generalizing, exploring whether different solution methods yield different insights, etc.? Or are those kinds of things not goals for you in teaching undergraduates? Dara Sandow At 11:30 PM -0700 3/7/05, Eldon McMurray wrote: >The following article is an example of using predominant learning >styles and Bloom' Taxonomy to teach mathematical reasoning. It is >the model all of our tutors are trained with. This has been very >helpful to our instructors as they mentor adjuncts. > >The WHAT, HOW, WHY, and WHAT IF of Mathematics: Teaching >undergraduates to think up Benjamin Blooms cognitive Levels > >By Carole Sullivan and Eldon McMurray of Utah Valley State College >To fully understand mathematics, it is important to know three things: > >1. WHAT precisely the problem is asking; >2. HOW to do the problem; and >3. WHY certain steps give you the correct answer. > >Then to consider this: WHAT IF the problem were a little different. >... _______________________________________________ PSTUM-list mailing list PSTUM-list(a)lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/pstum-list

19 years, 1 month

Re: Motivating grad students to teach thinking in Math simply

by Eldon McMurray

The following article is an example of using predominant learning styles and Bloom' Taxonomy to teach mathematical reasoning. It is the model all of our tutors are trained with. This has been very helpful to our instructors as they mentor adjuncts. The WHAT, HOW, WHY, and WHAT IF of Mathematics: Teaching undergraduates to think up Benjamin Blooms cognitive Levels By Carole Sullivan and Eldon McMurray of Utah Valley State College To fully understand mathematics, it is important to know three things: 1. WHAT precisely the problem is asking; 2. HOW to do the problem; and 3. WHY certain steps give you the correct answer. Then to consider this: WHAT IF the problem were a little different. Think about it. Can you really know how to work a problem if you don’t know what the problem is asking you to do? Can you really be sure that the how will produce the correct answer if you don’t understand why the steps work? It’s like trying to ride a bike for the first time without knowing what “ride” means. If you hadn’t seen someone ride a bike before, you likely would not understand this simple task: Ride the bike from point A to point B. You would first need to figure out what it means to “ride a bike.” So, let’s say this is what it means: To ride a bike is the act of making the bike move. That’s a good start, but how do you make the bike move? You might come up with the following steps: 1) Sit on the bike; 2) Put a foot on each pedal; 3) Push the pedals forward with your feet; 4) Grip the handle bars in your hands; 5) Keep the front tire straight until an obstruction compels you to turn, and so on. Now you know how to move the bike: Pedaling. Can you really be sure that pedaling will move the bike from point A to point B? You could jump on and give it a try. But could you be sure otherwise? No. You must know why the tires rotate when you push the pedals to understand how the bike moves (the pedals move the chain, the chain moves the tires, and the tires move the bike). To fully understand a problem, it is best to know the how, or the steps, and the why, the reason those steps work. “But I was so young when I learned to ride a bike,” you might say, “the hows or whys never even crossed my mind.” Fair enough. Like most of us, you just did what you saw everyone else doing and it worked. This is where the question what if comes in. At first, you probably didn’t wonder, “What if the bike won’t move when I push the pedals?” At some point, though, that very thing probably happened*the chain came off, and when it did you were obliged to think about how the bike moves and why so that you could fix it. Along the same lines, real success in math depends on more than just knowing how to get the right answer. Students arrive at correct answers all the time without really understanding mathematics. But if they get the right answer and don’t know what they were trying to accomplish or why their answer is right, have they learned the math? No, not really. “But all I’ve ever learned was how to do a math problem,” you might say, “and that’s gotten me through every math class just fine.” Point taken. Here’s the bad news, though. You can ignore the what, why, and what if for a while inside the classroom, but it’s probably going to catch up to you more quickly outside the classroom. Consider the following scenario outside of mathematics. Imagine that you have graduated from college and are working in your chosen field. Regardless of the occupation, your employer will want you to be able to solve problems. Maybe not algebra problems, but problems nevertheless! When you are given a problem, are you going to jump right into solving it? No, of course not. If you’re smart, you’ll analyze the problem first, make sure you understand what the problem is and what kind of answer is required. Once you fully understand what the problem is, then you are ready to tackle how to solve it. As you explore possibilities for achieving your goal, you will want to be aware of your resources. You may come up with a brilliant solution, only to find that the solution does not fit within the company’s budget. You need to know what you have to work with. Once you find a solution, your boss will ask you to explain why it will produce the desired outcome. No company wants to waste time and money on an iffy plan. You will need to be prepared to justify each step of your plan. And your boss won’t go for justification like, “Because I say it will work” or “Because my professor said it would work.” Your boss will likely ask many what ifs. What if questions help you consider and prepare for potential problems that may arise. Your boss will want to know that you have not only foreseen possible roadblocks but have devised a plan for how to deal with them. If you really want to impress your boss, you’ll be prepared with answers for every what if thrown your way. Do you see the importance of What, How, Why, and What If? Clearly, you can get in real trouble real fast in the real world when you ignore these vital questions. In the mathematics classroom, it may not seem to matter much until you get into a tough course. But it will catch up to you in here just like out there. Want to give the questions a try? The following is a basic example to get you started. EXAMPLE ONE Evaluate: What is the problem asking me to do? Evaluate What does that mean? Find the number that it is equal to. What rule will help me? Order of Operations What are operations? Addition, subtraction, multiplication, and division What is the Order of Operations? Work all problems in the following order: 1-Operations inside grouping symbols ( ) 2-Exponents*powers 3-Multiplication and division left to right 4-Addition and subtraction left to right How do I work the problem? Start inside the parentheses. Why? Order of Operations How do I do what is inside the parentheses? Do the division first then the subtraction. Why? Order of Operations Why is the 6 still in parentheses? Is this necessary? Yes. Parentheses can also be a symbol for multiplication. What does the problem look like now? What is the next step? Multiply and then add. How do I know that is correct? The Order of Operations was followed. What if the answer is a decimal or fraction? Decimals and fractions are possible answers, but if you haven’t worked with them previously in the class then the answer is probably wrong*go back and check your work. What if it doesn’t seem to follow Order of Operations? Remember that operations may be implied*meaning that you don’t see a specific symbol, but you’re supposed to know what to do. See the following example: Evaluate: How do I work the problem? Start with the operations in grouping symbols. Why? There don’t seem to be any grouping symbols. Remember that when the numerator or denominator of a fraction contains an operation, there are implied grouping symbols. So What next? Divide. Why? I don’t see a division symbol. Remember that a fraction is another way to represent division. This may seem like a lot of work for a fairly short problem, but understanding the problem thoroughly will help you with longer, more difficult problems that you will encounter later on. Don’t focus on finishing the problem in the shortest possible time. Focus instead on understanding all aspects of the problem. You’ll save time in the long run. Here are two more examples: EXAMPLE TWO Simplify: What is the problem asking me to do? Simplify What does that mean? Reduce the number of terms. What is a term? A number, variable, or a number and variable(s) being multiplied. How can I reduce the number of terms? Use the distributive property of multiplication over addition. What is that property? How does that apply to this problem? Using this property the problem can be written as The coefficients (numbers in front of the variables) can be grouped in parentheses followed by the x. Thus the rule is to add the coefficients and keep the same variable. How do I know that is correct? Check it by using a specific number for x. Say . (or any number you choose) Then Both expressions equal 60 so is correct. What if the variables are different? The distributive property cannot be applied and thus the expression cannot be simplified. Example: How can the terms be combined? They can’t because the distributive property cannot be used: Neither x nor y can replace the ? to make a true statement. So cannot be simplified. What if some terms have the same variable but others don’t? Example: How can I simplify this problem? Group the like terms. What are like terms? Terms with the same variable(s) raised to the same power(s). How can I group terms that aren’t already side by side? Use the commutative property of addition to order the terms in any way. What next? Apply the distributive property to the like terms. How do I know this is correct? Check it by using and (or any other numbers that you choose) EXAMPLE THREE Solve: What is the problem asking me to do? Solve What does that mean? Find the number that can replace x and make the equation true. How can I find x? First simplify. (Reduce the number of terms.) Then get x by itself. Why simplify? To make the problem easier to work with. How do I simplify? Apply the distributive property and combine like terms. How can I get x by itself? Add 2 to both sides and then divide both sides by -2. Why? The Properties of Equality say that adding the same number to both sides of an equation or dividing both sides of an equation by the same number will not change the solution. How do I know that is correct? Check it. When x is replaced with -4 the equation is true. What if the equation is not true? The answer could be extraneous, meaning you haven’t made any mistakes, the answer simply is not a solution. Or (more likely) you made a mistake. Either way, go back and double check your work. What if there is a variable on both sides of the equation? Example: How can I find x? First simplify. What next? Use the properties of equality to isolate the x. How? Add 3x to both sides and add 8 to both sides. What is x? because How do I know this is correct? Check it in the original equation. This is a true statement so is the correct solution. As you can see, after you determine what the problem is asking you to do, you can ask How, Why and What If in any order. And don’t get caught up in whether to ask what or why*just start asking questions! Have a reason for every step that you take in a problem, and imagine that you have to explain your reasons. (It will be good practice for explaining solutions to your future boss.) Try to anticipate every different kind of problem that your teacher could throw your way. And you won’t be stumped! By asking these key questions, mathematics can change from the daunting task of memorizing a jumbled mess of rules and formulas to a clearly marked path where every step you take has purpose and meaning. Eldon L. McMurray Director Faculty Center for Teaching Excellence Assistant Professor College Success & Academic Literacy Utah Valley State College 800 West University Parkway Orem, UT 84058 (801) 863-8550 >>> "Kenneth P. Bogart" <Kenneth.P.Bogart(a)dartmouth.edu> 03/07/05 2:14 PM >>> --- You wrote: 5) Focus Also on Careers Two ideas we had here concern career-minded TAs. One idea we had was to contact former graduate students who have now gone onto academic jobs and ask them to share about the role of teaching in their current careers. Sharing these "testimonies" with the current TAs in some way might help them see the value of spending time developing their teaching skills. Also, we thought we might add some teaching-related career-oriented topics, such as writing teaching philosophy statements and building teaching portfolios. --- end of quote --- These are very good, because they hit the TA's where they are going to live. My memory is that you have a teaching evaluation system that applies to the graduate students. You can use it to motivate students to participate. We have one that we use for everyone who teaches, and though it is voluntary for senior faculty, most participate most of the time. Early on in our seminar, if I am involved in it, I mention to graduate students that the vast majority of our graduate students get overall teaching ratings higher than the department average. (This isn't a Lake Woebegone phenomenon; our visitors, postdocs, and most regular faculty are in those averages.) In the most understated way I can, I point out how easy it is for the writer to a teaching letter to say "So and So's average on the "overall how do you rate this teacher" question is 4.25 on a 1 to 5 scale with 5 being the best, while the department average is about 4.1," and mention the impact that has on someone's chances for a job interview at a liberal arts college or a university where teaching is the main faculty function. I don't want to push the idea too hard, because I have seen very good teachers with below average ratings. But everything you can do to positively link your seminar with students' job opportunities later in life is likely to have an impact on their commitment to the seminar. _______________________________________________ PSTUM-list mailing list PSTUM-list(a)lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/pstum-list

19 years, 1 month

Re: [PSTUM-list] Motivating grad students

by Kenneth.P.Bogart＠Dartmouth.EDU

--- You wrote: 5) Focus Also on Careers Two ideas we had here concern career-minded TAs. One idea we had was to contact former graduate students who have now gone onto academic jobs and ask them to share about the role of teaching in their current careers. Sharing these "testimonies" with the current TAs in some way might help them see the value of spending time developing their teaching skills. Also, we thought we might add some teaching-related career-oriented topics, such as writing teaching philosophy statements and building teaching portfolios. --- end of quote --- These are very good, because they hit the TA's where they are going to live. My memory is that you have a teaching evaluation system that applies to the graduate students. You can use it to motivate students to participate. We have one that we use for everyone who teaches, and though it is voluntary for senior faculty, most participate most of the time. Early on in our seminar, if I am involved in it, I mention to graduate students that the vast majority of our graduate students get overall teaching ratings higher than the department average. (This isn't a Lake Woebegone phenomenon; our visitors, postdocs, and most regular faculty are in those averages.) In the most understated way I can, I point out how easy it is for the writer to a teaching letter to say "So and So's average on the "overall how do you rate this teacher" question is 4.25 on a 1 to 5 scale with 5 being the best, while the department average is about 4.1," and mention the impact that has on someone's chances for a job interview at a liberal arts college or a university where teaching is the main faculty function. I don't want to push the idea too hard, because I have seen very good teachers with below average ratings. But everything you can do to positively link your seminar with students' job opportunities later in life is likely to have an impact on their commitment to the seminar.

19 years, 1 month

Re: motivating grad students

by Joanne Nakonechny

Derek: Seminar attendance is always an issue as other demands are always present. Having said this, food is always a nice attractor. Faculty encouragement also helps graduate students understand that teaching IS important. Nothing like having a faculty member saying something like, "Shouldn't you be spending some more time on your research rather than going to that workshop?" to really get the message across that teaching is not important. Perhaps another element in all of this is a notion of ownership. Your topics look great, and I would love to attend them, but maybe the students don't have a sense of having their questions answered. Could you have an initial meeting at the beginning of the year, made up of faculty and grad students, to talk about the importance of teaching and ask them (grad students) about the topics they would like to have in the first semester? Another possibility would be to include faculty in the sessions as well to underline the idea that teaching is important. (This idea of including faculty may or may not be a good idea given issues of peer development, but it might work.) Just some thoughts.... Good luck! Joanne pstum-list-request(a)lists.fas.harvard.edu wrote: >Send PSTUM-list mailing list submissions to > pstum-list(a)lists.fas.harvard.edu > >To subscribe or unsubscribe via the World Wide Web, visit > http://lists.fas.harvard.edu/mailman/listinfo/pstum-list >or, via email, send a message with subject or body 'help' to > pstum-list-request(a)lists.fas.harvard.edu > >You can reach the person managing the list at > pstum-list-owner(a)lists.fas.harvard.edu > >When replying, please edit your Subject line so it is more specific >than "Re: Contents of PSTUM-list digest..." > > >Today's Topics: > > 1. luring graduate students. (Bruce Reznick) > 2. Re: Motivating grad students (Kenneth P. Bogart) > 3. Re: Motivating Graduate Students (S. Hauk) > > >---------------------------------------------------------------------- > >Message: 1 >Date: Mon, 21 Feb 2005 11:13:07 -0600 (CST) >From: Bruce Reznick <reznick(a)math.uiuc.edu> >Subject: [PSTUM-list] luring graduate students. >To: <pstum-list(a)lists.fas.harvard.edu> >Message-ID: > <Pine.GSO.4.33.0502211102160.8735-100000(a)u52.math.uiuc.edu> >Content-Type: TEXT/PLAIN; charset=US-ASCII > >Derek -- > >Our graduate director is a big believer in pizza, soda and other free >food. In an ideal world, bribery wouldn't be necessary, but you asked. > >I guess I should introduce myself. I'm essentially a research >mathematician who has always had a strong interest in good teaching, even >in the bad old days of the 70's and 80's, when those interests were >thought to be mutually exclusive. [Two true stories from those days: >In my first week of my first job, another newly hired colleague asked >"You seem to like teaching, why didn't you try to get a job at a >4-year school". The first time my Head nominated me for a teaching >award, a concerned senior colleague asked me if that meant I wasn't >getting tenure.] > >After I got tenure in `84, I wrote a teaching guide for our grad student >orientation, and after several incaranations, it currently resides at > >http://www.math.uiuc.edu/~reznick/ciu.html > >Comments are always welcome; I ought to do another version before I >retire. When it comes to teaching advice, I'm full of it. > >-- Bruce > >On Mon, 21 Feb 2005 pstum-list-request(a)lists.fas.harvard.edu wrote: > > > >>Send PSTUM-list mailing list submissions to >> pstum-list(a)lists.fas.harvard.edu >> >>To subscribe or unsubscribe via the World Wide Web, visit >> http://lists.fas.harvard.edu/mailman/listinfo/pstum-list >>or, via email, send a message with subject or body 'help' to >> pstum-list-request(a)lists.fas.harvard.edu >> >>You can reach the person managing the list at >> pstum-list-owner(a)lists.fas.harvard.edu >> >>When replying, please edit your Subject line so it is more specific >>than "Re: Contents of PSTUM-list digest..." >> >> >>Today's Topics: >> >> 1. Motivating grad students (Derek Bruff) >> >> >>---------------------------------------------------------------------- >> >>Message: 1 >>Date: Mon, 21 Feb 2005 11:10:07 -0500 >>From: Derek Bruff <bruff(a)fas.harvard.edu> >>Subject: [PSTUM-list] Motivating grad students >>To: Preparing and Supporting Teachers of Undergraduate Mathematics >> <pstum-list(a)lists.fas.harvard.edu> >>Message-ID: <BE3F720F.534A%bruff(a)fas.harvard.edu> >>Content-Type: text/plain; charset="US-ASCII" >> >>PSTUM-List, >> >>This year we have been running a seminar on teaching undergraduate >>mathematics designed to help our graduate students improve our teaching. >>The seminar is optional, and attendance has generally been low. I'm >>wondering if anyone on the list has experience with attendance-optional, >>math department teaching seminars. What, if anything, have you found >>particular effective in motivating graduate students to attend? >> >>If it helps, here's the seminar's web site: >> >>http://abel.math.harvard.edu/preceptor/tums/ >> >>Thanks in advance for your help! >> >>Derek >> >>-- >>Derek Bruff, Preceptor >>Department of Mathematics, Harvard University >>Email: bruff(a)fas.harvard.edu >>Web: http://www.derekbruff.com/ >> >> >> >> >>------------------------------ >> >>_______________________________________________ >>PSTUM-list mailing list >>PSTUM-list(a)lists.fas.harvard.edu >>http://lists.fas.harvard.edu/mailman/listinfo/pstum-list >> >> >>End of PSTUM-list Digest, Vol 2, Issue 17 >>***************************************** >> >> >> > > > >------------------------------ > >Message: 2 >Date: 21 Feb 2005 14:45:44 EST >From: Kenneth.P.Bogart(a)Dartmouth.EDU (Kenneth P. Bogart) >Subject: Re: [PSTUM-list] Motivating grad students >To: pstum-list(a)lists.fas.harvard.edu, pstum-list(a)lists.fas.harvard.edu > (Preparing and Supporting Teachers of Undergraduate Mathematics) >Cc: Kim Rheinlander <Kim.Rheinlander(a)Dartmouth.EDU> >Message-ID: <50263244(a)newvixen.Dartmouth.EDU> >Content-Type: text/plain > >Hi All. I think my earlier attempt at a post was before the listserve was >actually running. So I'll begin with my introduction. > >I'm Ken Bogart. My only full-time job has been teaching at Dartmouth since >1968. My research for years has been in various branches of combinatorics, but >around 1995 I caught the bug of wanting to apply research in how people learn >mathematics to the teaching of undergraduates. (This was the resul of being >asked to participate in our teaching seminar, described below). Over the years >this has changed my research agenda and I now think of research in how >undergraduates learn mathematics as my primary interest. > >My short answer to Derek's post is that unless students perceive the seminar as >a more important use of their time than preparing for qualifying exams or >writing a thesis, the only hope is, as Bruce Resnick suggests, to bribe them >with food. But in the long run, if the tradeoff of food for time cuts into what >they perceive as the department's top priorities for them, they will stop >participating. In our department we have flexible rules and inflexible rules >for graduate students. The three most inflexible rules are > >1. You have to write (and successfully defend) a thesis. > >2. You have to teach at least two (ten week) courses on your own, and to be >allowed to do so, you must take the teaching seminar. > >3. You have to pass qualifying exams in a timely way. > >I list them in this order, because the timeliness of the teaching seminar is >less flexible than the timliness of qualifying exams. We have been consistent >in enforcing requirement 2 so that it is now a part of our graduate student >culture that this is something everyone does and it is part of our faculty >culture that we cut our thesis advisees slack when they are in the teaching >seminar or when they are teaching their courses. > >Dartmouth has had some sort of teaching seminar since the mid seventies. It >began as an opportunity for (second year) grad students who were about to teach >on their own to give two one-hour practice lectures with 3 faculty and all the >other second year graduate students attending and trying to act like >undergraduates. Eventually it was undermined significantly when a senior >faculty member who was chair of the seminar committee decided fifteen minute >lectures were long enough. After that it was hard to bring up issues of student >involvement, etc., because there wasn't enough time for the grad students to >really get going in their practice lectures. In the late eighties when I was >chair, faculty members Dorothy Wallace and Marcia Groszek wrote a proposal with >Claudia Henrion from Middlebury to FIPSE to desing a seminar that would use the >research literature of math education as a basis for a required summer-long >seminar (with lots of practical experience) for all grad students who were going >to begin teaching the following year. It ended up getting funded by Pew >Foundation, and the department approved the plan that resulted: The graduate >teaching seminar at Dartmouth is effectively a ten quarter-hour graduate course >in which graduate students who are preparing to be undergraduate teachers read >and discuss the literature of how undergraduates (and others) learn mathematics, >prepare and run two one-week workshops for high school students (in which they >attempt to put what they have gleaned from the research literature into >practice), engage in practice of various skills that are hoped to be useful to >them in teaching, practice teach in two one-hour classes that are being run by >other faculty members in Dartmouth's summer term, and reflect on their >activities. We make heavy use of videotape to give the grduate students fodder >for reflection. > >When I stopped being chair, I was recruited to join the seminar teaching staff >as part of Dartmouth's Math Across the Curriculum grant. (It funded two >teachers for the seminar for five years, and allowed Dorothy, Marcia, and then >me to train several other faculty members in the methods.) > >I don't recall any complaints about graduate student teaching since we >instituted the seminar. It is required of all students when they make the >transition at the end of the second year from being TAs to being in charge of >their own courses or sections of courses. > > The administrator for the seminar is Kim Rheinlander at Dartmouth, and >information about the seminar is available from her or from any of the above >faculty members. Visitors, either short-term or long-term, >including a limited number of graduate students from other institutions, are >welcome. In particualr, we are happy to have faculty members from other >institutions not only observe but co-teach the seminar in order to become >familiar with our methods. We have a long range project of creating a web-page >for the seminar, but that has so far fallen victim to our perceptions about our >own institution's priorities for faculty members! > >Ken Bogart > > >------------------------------ > >Message: 3 >Date: Mon, 21 Feb 2005 18:29:09 -0700 >From: "S. Hauk" <hauk(a)unco.edu> >Subject: [PSTUM-list] Re: Motivating Graduate Students >To: pstum-list(a)lists.fas.harvard.edu >Message-ID: <2652A3A2-8471-11D9-8E5A-000A95AEF880(a)unco.edu> >Content-Type: text/plain; charset=US-ASCII; format=flowed > >Hi, > A few suggestions: >1. The meetings should be on a predictable, REGULAR BASIS so that grad >students can plan to attend (modeling one of the important strategies >for successful teaching: Planning). This is not the same as regularly >announcing an irregularly scheduled meeting (e.g., always announcing a >meeting two weeks in advance). > >2. Make clear in announcements what kind of INFORMATION AND ACTIVITIES >can be expected (from what I see on the web, only the information part >of this is generally offered). > >3. Another key to increasing attendance is DISTRIBUTION. Remind >teaching faculty (not just grad students) that the regularly scheduled >meeting is coming up in 7 days and in 2 days. Do this on the web, >through email, and on flyers. For flyers, choose a distinctive color >for the teaching seminar and always put teaching seminar flyers on this >same color. These flyers should be BOTH: distributed to mailboxes AND >posted in places frequented by teaching faculty (e.g., over every copy >machine in the department - give them something to read in that >photo-copy-zen state of mind). Also, remove the flyer as soon as the >meeting is over or post flyers that list SEVERAL upcoming meetings and >leave in place for a long time (the first strategy is actually more >likely to generate attendance, since the old flyer disappears and a >blank spot on the wall exists for a bit before the new flyer is posted). > >4. Personally invite five people to the meeting, one at a time. For >each who promises to attend, ask them to commit to bringing a friend. > >Shandy > > > >------------------------------ > >_______________________________________________ >PSTUM-list mailing list >PSTUM-list(a)lists.fas.harvard.edu >http://lists.fas.harvard.edu/mailman/listinfo/pstum-list > > >End of PSTUM-list Digest, Vol 2, Issue 18 >***************************************** > > -- Joanne Nakonechny, Ph.D. Senior Research Associate Science Centre for Learning and Teaching (Skylight), Faculty of Science #175-6221 University Boulevard Vancouver, B.C. Canada V6T 1Z1 Tel: 604-822-4691 Fax: 604-822-4282 E-mail: nakonechny(a)science.ubc.ca

19 years, 2 months

Re: Motivating Graduate Students

by S. Hauk

Hi, A few suggestions: 1. The meetings should be on a predictable, REGULAR BASIS so that grad students can plan to attend (modeling one of the important strategies for successful teaching: Planning). This is not the same as regularly announcing an irregularly scheduled meeting (e.g., always announcing a meeting two weeks in advance). 2. Make clear in announcements what kind of INFORMATION AND ACTIVITIES can be expected (from what I see on the web, only the information part of this is generally offered). 3. Another key to increasing attendance is DISTRIBUTION. Remind teaching faculty (not just grad students) that the regularly scheduled meeting is coming up in 7 days and in 2 days. Do this on the web, through email, and on flyers. For flyers, choose a distinctive color for the teaching seminar and always put teaching seminar flyers on this same color. These flyers should be BOTH: distributed to mailboxes AND posted in places frequented by teaching faculty (e.g., over every copy machine in the department - give them something to read in that photo-copy-zen state of mind). Also, remove the flyer as soon as the meeting is over or post flyers that list SEVERAL upcoming meetings and leave in place for a long time (the first strategy is actually more likely to generate attendance, since the old flyer disappears and a blank spot on the wall exists for a bit before the new flyer is posted). 4. Personally invite five people to the meeting, one at a time. For each who promises to attend, ask them to commit to bringing a friend. Shandy

19 years, 2 months

Re: [PSTUM-list] Motivating grad students

by Kenneth.P.Bogart＠Dartmouth.EDU

Hi All. I think my earlier attempt at a post was before the listserve was actually running. So I'll begin with my introduction. I'm Ken Bogart. My only full-time job has been teaching at Dartmouth since 1968. My research for years has been in various branches of combinatorics, but around 1995 I caught the bug of wanting to apply research in how people learn mathematics to the teaching of undergraduates. (This was the resul of being asked to participate in our teaching seminar, described below). Over the years this has changed my research agenda and I now think of research in how undergraduates learn mathematics as my primary interest. My short answer to Derek's post is that unless students perceive the seminar as a more important use of their time than preparing for qualifying exams or writing a thesis, the only hope is, as Bruce Resnick suggests, to bribe them with food. But in the long run, if the tradeoff of food for time cuts into what they perceive as the department's top priorities for them, they will stop participating. In our department we have flexible rules and inflexible rules for graduate students. The three most inflexible rules are 1. You have to write (and successfully defend) a thesis. 2. You have to teach at least two (ten week) courses on your own, and to be allowed to do so, you must take the teaching seminar. 3. You have to pass qualifying exams in a timely way. I list them in this order, because the timeliness of the teaching seminar is less flexible than the timliness of qualifying exams. We have been consistent in enforcing requirement 2 so that it is now a part of our graduate student culture that this is something everyone does and it is part of our faculty culture that we cut our thesis advisees slack when they are in the teaching seminar or when they are teaching their courses. Dartmouth has had some sort of teaching seminar since the mid seventies. It began as an opportunity for (second year) grad students who were about to teach on their own to give two one-hour practice lectures with 3 faculty and all the other second year graduate students attending and trying to act like undergraduates. Eventually it was undermined significantly when a senior faculty member who was chair of the seminar committee decided fifteen minute lectures were long enough. After that it was hard to bring up issues of student involvement, etc., because there wasn't enough time for the grad students to really get going in their practice lectures. In the late eighties when I was chair, faculty members Dorothy Wallace and Marcia Groszek wrote a proposal with Claudia Henrion from Middlebury to FIPSE to desing a seminar that would use the research literature of math education as a basis for a required summer-long seminar (with lots of practical experience) for all grad students who were going to begin teaching the following year. It ended up getting funded by Pew Foundation, and the department approved the plan that resulted: The graduate teaching seminar at Dartmouth is effectively a ten quarter-hour graduate course in which graduate students who are preparing to be undergraduate teachers read and discuss the literature of how undergraduates (and others) learn mathematics, prepare and run two one-week workshops for high school students (in which they attempt to put what they have gleaned from the research literature into practice), engage in practice of various skills that are hoped to be useful to them in teaching, practice teach in two one-hour classes that are being run by other faculty members in Dartmouth's summer term, and reflect on their activities. We make heavy use of videotape to give the grduate students fodder for reflection. When I stopped being chair, I was recruited to join the seminar teaching staff as part of Dartmouth's Math Across the Curriculum grant. (It funded two teachers for the seminar for five years, and allowed Dorothy, Marcia, and then me to train several other faculty members in the methods.) I don't recall any complaints about graduate student teaching since we instituted the seminar. It is required of all students when they make the transition at the end of the second year from being TAs to being in charge of their own courses or sections of courses. The administrator for the seminar is Kim Rheinlander at Dartmouth, and information about the seminar is available from her or from any of the above faculty members. Visitors, either short-term or long-term, including a limited number of graduate students from other institutions, are welcome. In particualr, we are happy to have faculty members from other institutions not only observe but co-teach the seminar in order to become familiar with our methods. We have a long range project of creating a web-page for the seminar, but that has so far fallen victim to our perceptions about our own institution's priorities for faculty members! Ken Bogart

19 years, 2 months

luring graduate students.

by Bruce Reznick

Derek -- Our graduate director is a big believer in pizza, soda and other free food. In an ideal world, bribery wouldn't be necessary, but you asked. I guess I should introduce myself. I'm essentially a research mathematician who has always had a strong interest in good teaching, even in the bad old days of the 70's and 80's, when those interests were thought to be mutually exclusive. [Two true stories from those days: In my first week of my first job, another newly hired colleague asked "You seem to like teaching, why didn't you try to get a job at a 4-year school". The first time my Head nominated me for a teaching award, a concerned senior colleague asked me if that meant I wasn't getting tenure.] After I got tenure in `84, I wrote a teaching guide for our grad student orientation, and after several incaranations, it currently resides at http://www.math.uiuc.edu/~reznick/ciu.html Comments are always welcome; I ought to do another version before I retire. When it comes to teaching advice, I'm full of it. -- Bruce On Mon, 21 Feb 2005 pstum-list-request(a)lists.fas.harvard.edu wrote: > Send PSTUM-list mailing list submissions to > pstum-list(a)lists.fas.harvard.edu > > To subscribe or unsubscribe via the World Wide Web, visit > http://lists.fas.harvard.edu/mailman/listinfo/pstum-list > or, via email, send a message with subject or body 'help' to > pstum-list-request(a)lists.fas.harvard.edu > > You can reach the person managing the list at > pstum-list-owner(a)lists.fas.harvard.edu > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of PSTUM-list digest..." > > > Today's Topics: > > 1. Motivating grad students (Derek Bruff) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Mon, 21 Feb 2005 11:10:07 -0500 > From: Derek Bruff <bruff(a)fas.harvard.edu> > Subject: [PSTUM-list] Motivating grad students > To: Preparing and Supporting Teachers of Undergraduate Mathematics > <pstum-list(a)lists.fas.harvard.edu> > Message-ID: <BE3F720F.534A%bruff(a)fas.harvard.edu> > Content-Type: text/plain; charset="US-ASCII" > > PSTUM-List, > > This year we have been running a seminar on teaching undergraduate > mathematics designed to help our graduate students improve our teaching. > The seminar is optional, and attendance has generally been low. I'm > wondering if anyone on the list has experience with attendance-optional, > math department teaching seminars. What, if anything, have you found > particular effective in motivating graduate students to attend? > > If it helps, here's the seminar's web site: > > http://abel.math.harvard.edu/preceptor/tums/ > > Thanks in advance for your help! > > Derek > > -- > Derek Bruff, Preceptor > Department of Mathematics, Harvard University > Email: bruff(a)fas.harvard.edu > Web: http://www.derekbruff.com/ > > > > > ------------------------------ > > _______________________________________________ > PSTUM-list mailing list > PSTUM-list(a)lists.fas.harvard.edu > http://lists.fas.harvard.edu/mailman/listinfo/pstum-list > > > End of PSTUM-list Digest, Vol 2, Issue 17 > ***************************************** >

19 years, 2 months

New Book on Adjuncts

by Derek Bruff

PSTUM List, I know several of you are interested in preparing and supporting adjuncts, and I thought you might want to be aware of a new book on this subject. The scope of the book is not limited to mathematics departments, and I haven't read the book, so I don't know how useful it is. But, nonetheless, here is some information on it. If you've read the book, it would be great if you could post a short review to the list. Thanks! Derek ADJUNCT FACULTY IN COMMUNITY COLLEGES An Academic Administrator¹s Guide to Recruiting, Supporting, and Retaining Great Teachers Desna L. Wallin, Editor Department chairs and deans are responsible for the hiring and direct supervision of adjunct faculty, but a number of factorssuch as lack of current teaching experience or preoccupation with other administrative functionsmay keep them from sufficiently providing for the needs of this critical group. This book provides department chairs and deans with examples of successful programs that are in place at a variety of community and technical colleges across the United States and that can be implemented into a two-year system. All examples are models of support for adjunct faculty and highlight the important connection between teaching quality and effective hiring, orientation, acculturation, and professional development practices for adjunct faculty. 6 x 9 $39.95 cloth 246 pp 2005 ISBN 1-882982-81-9 For more details or to order, point your web browser to: https://secure.aidcvt.com/ank/ProdDetails.asp?ID=1882982819&PG=1&Type=BL -- Derek Bruff, Preceptor Department of Mathematics, Harvard University Email: bruff(a)fas.harvard.edu Web: http://www.derekbruff.com/

19 years, 2 months

Re: Participant permission to use video data

by S. Hauk

Hi, So, an important issue to concern ourselves with in any collecting of video (or audio) data is what the federal government regulations calls "research with human subjects." Federal guidelines are the minimum collection to which institutions that receive any federal or state funding must conform. The quotes below are from the Code of Federal Regulations, Title 45 - Public Welfare, Part 46 - Protection of Human Subjects < http://www.hhs.gov/ohrp/humansubjects/guidance/45cfr46.htm >. "Research means a systematic investigation, including research development, testing and evaluation, designed to develop or contribute to generalizable knowledge. Activities which meet this definition constitute research for purposes of this policy, whether or not they are conducted or supported under a program which is considered research for other purposes. For example, some demonstration and service programs may include research activities." In other words: collecting video data in a classroom and using it to train other teachers can be considered "research" for the purposes of the regulation. Consequently, it may be necessary, depending on the Institutional Review Board (or its equivalent) at your institution, to obtain written permission from anyone whose image, voice, name, or other identifiable information can be ascertained from the video. Interpretations of the statutes are sometimes broad and sometimes narrow, depending on local, state, and institutional guidelines. The issue of protection of human subjects is an important one and is taken very seriously by the legal-eagles at most institutions. I suggest you consult with the chair of your institutional IRB to find out what sort of permissions (if any) they feel are appropriate before sharing video data. It turns out that for the video-case materials I am developing, I am required to obtain a liability release from each person in the room when the video data is captured in order to use the actual video on a nationally released, commercially available, product. Shandy On Saturday, February 12, 2005, at 10:00 AM, Derek wrote: >> Derek, >> I have a couple of questions, first: >> 1. How did you secure liability release from all the people in >> your video >> clips so that they could be used in your TA training? > > I received permission from the teachers involved to use the footage > for the > purposes of TA training. Is there more needed? >

19 years, 2 months

introduction: Gary Harris

by Harris, Gary

Dear Colleagues, My name is Gary Harris and I am the Director of Undergraduate Programs in the Department of Mathematics and Statistics at Texas Tech University. In the spring of 2000 I was asked by our chair and the director of graduate programs to create a 3 credit hour course devoted to issues involving teaching math at the undergraduate level. I would like to say that this was motivated for all the obvious great reasons; however, I suspect the main motivation was the fact that our state regulatory agency requires that all instructors of record (aka actual teachers of the classes) for college level math classes have at least 18 hours of graduate level mathematics credit, and our university decided to get serious about adhering to this rule. Hence this would be one way for our new TA's to get an extra 3 hours graduate math credit their first semester, while at the same time maybe picking up something useful. In any event I began to look for appropriate materials and activities and was ready to offer the course to 20 new teaching assistants in the fall of 2000. The course has been offered each fall semester thereafter. Early on I helped to field test some of Friedberg's case studies and have used them regularly. I also use material from Rishel's Handbook for Mathematics Teaching Assistants, as well as other materials. Also a significant part of the course involves video taping and class evaluations of student mini-lectures. I currently have a graduate student working on a Masters Thesis in which he is trying to assess the effects of our course on our graduate students attitudes and practice with regard to teaching mathematics at the college level. He and I would be very interested to hear about experiences any of you may have with such a course, as well as pertinent references. I look forward participating in an interesting discussion on this timely and, I think, very important topic, Gary Harris

19 years, 2 months

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