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Fall 2016 Info: How to Teach Mathematics

Fall 2016 Book: Stephen G. Krantz, How to Teach Mathematics (3rd Ed.), published by the AMS (American Mathematical Society), 2015. This an update from earlier editions published in 1993 and 1999.

Book Availability: KCTL has a supply of books for our fall reading. If you can commit to joining at least two of our fall discussion meetings, then you can pick up a book for free in M-391.

Discussion Meetings: Mondays, 11:30 AM – 12:30 PM, in M-391 on the following dates.

  • Sep-26: Ch. 1-2, “Guiding principles”, “Practical matters”.
  • Oct-24: Ch. 3-4, “Spiritual matters”, “The electronic world”.
  • Nov-21: Ch. 5-6, “Difficult matters”, “A new beginning”.

More Optional Readings: Available online.

CUNY Central Recommendations; Spacing Study; Online Homework

Discussing:

Announcements: Funding available for STEM learning conferences (contact Kristen).

(1) What Faculty Expect to Gain From Attending Conferences

Networking, collaborations, new research, present research & get feedback.

(2) CUNY Central Academic Affairs

Initiative to move away from remediation as a majority of what we offer; integrate remediation into credit-bearing courses (e.g., LaGuardia & Guttman).

Is this a national trend? (We don’t know, but sense that CUNY is at the vanguard.)

If math/QR (quantitative reasoning) requirements are diluted or done away with, at what point do you cross over from being a university to being a technical college like Monroe?

The effect on graduation rates is at the heart of this.

New requirements: (1) Allow calculators on tests; (2) Give non-algebra course to non-STEM students; (3) Pass algebra students even if they fail the final.

Effects on transferability outside CUNY? Will this influence CUNY Central?

(3) Discussion of CUNY “Best Teaching Practices” Document

Suggestion about studying in different environments; the study referenced is probably not vaild as evidence for this practice.

When this was brought up to CUNy Central, their response was that they would not remove this suggestion until a study is done supporting the opposite (essentially, “prove the null hypothesis”). A local survey of students showed that those who did study in different environments showed no effect on overall grade or final exam scores (unpublished).

(4) Discussion of Carpenter Article on Spacing

Many of us thought this might support (3) above by showing that different environments may not be best. But instead it was about the timing of learning — gaps between presentation, review, and test.

(5) Discussion of Options for Online Homework

(E.g.: Software packages including textbook & online homework)

ALEKS — Math, chemistry, physics (K-12 as well as college; www.aleks.com).

Challenges with using online homework/effectiveness for student success.

 

First Class Visit; Nehm Paper; Dunlosky Paper

Discussing:

Attending: Patrick, Daniel, Kristen, Emral, Shoshana.

(1) Daniel’s visit to Shoshana’s class

They had discussed interspersing lecture and practice, every 30 min (20 min/10 min respectively). Shoshana had been doing both, but with larger intervals. She thought the shorter intervals have been more effective since then.

Discussion of how the programming software shows you what each line of code is doing as it does it (jGRASP debugger).

(2) Ross Nehm article

Issues with problem-solving skills; identifying relevant information to use to solve the problem.

Textbooks — do not much help students to organize new info like an expert. Could OER help?

Describes well how students need to “deactivate” irrelevant info — how can instructors help? Use in-class activities to individually diagnose & resolve with each student. Showing the class an incorrect response often lodges it in everyone’s mind — so that’s less effective.

(3) “What Works, What Doesn’t” article

Useful tips to share with students.

McGraw-Hill online texts — do electronic highlighting?!

Highlighting emphasizes key terms, but ignores/makes invisible the connections, which is what an expert hones in on.

Self-testing (which is basically doing the homework) is what works. Teachers know this works, but do students?

Making a chart with connections is harder homework than the questions at the end of the chapter, but more effective.

Assessing students’ mastery not just of concepts, but of organization & connections (expertise, with the concepts). Such assessment can be difficult to explain to students what they did “wrong”. “That’s not what I meant” (said by students); they need to articulate what they understand, in a more precise, expert way.

Giving students examples of graded work prior to formally assessing them can help.

Brief discussion of physical set-up of the room — digital projection AND two whiteboards necessary for STEM classes. Desired: splitter for two screens (presenter view, presentation view).

 

Freeman on Linear Regression, Active Learning; Pairs for Observations

Discussing:

Attending: Kristin, Tara, Jennifer, Daniel, Emral, Azure, Patrick, Shoshana.

Explained proposal to informally observe one another’s classes & teaching strategies this semester. Will assign pairs to work together.

(1) Linear Regression Paper

In our own experience, nonrandom student enrollment and other factors such as instructor do affect any conclusions about effects of interventions.

In assessment, factors such as GPA might need to be collected to validate conclusions (here, at KCC).

Will adoption of these methods reduce the number of “publishable” studies (those finding an effect of interventions)? Would this be a disincentive to use these methods? (Depends on the editors of the journals & whether they’re aware of this issue.)

(2) Active Learning Paper

A bit melodramatic, considering the broad definition of active learning — who doesn’t do at least some of this each lecture?

Some concepts require worked examples and relatively longer explanation (as discussed in a previous semester).

Active learning can often seem to improve learning, but mask a deeper misconception until later.

Experience with students analyzing probability of life on Mars, but not actually understanding what a molecule is.

“Black box” or abstract concepts are not interesting to students (by their own report).

Tangible concepts, or at least tangible models, seem to help most students. But, abstract thinking can be critical to new insights. So how do we encourage/teach/help them practice abstract thinking?

Most, maybe all beginning students just learn the “mechanics” — definitions, procedures — without necessarily deeply understanding the concepts at first.

Students in the elementary algebra class, required to “double-check” answers by plugging in your solution & seeing if it comes out as it should. This is shown/practiced in class, but on the exam, students are perplexed by how to do/interpret (particularly how to do the check). This is interesting: What is the issue? Can we identify it? Do they really understand what “equals” means? This is a major problem in math, and a predictor of success. Focusing on “equals” in class/or focusing on checks, has not made a difference yet.

Focusing on some concept in class, including an active-learning exercise, sends a message to students that it’s important.

(3) Pairings for Observation

  • Daniel – Shoshana
  • Emral – Azure
  • Kristin – Pat
  • Tara & Jen to visit Daniel’s M2 class

Pairs to email each other to arrange; discuss next time.

 

Readings for Spring 2016

1st Session

  • Freeman, Scott, et al. “Active learning increases student performance in science, engineering, and mathematics.” Proceedings of the National Academy of Sciences 111.23 (2014): 8410-8415. (Link)
  • Theobald, Roddy, and Scott Freeman. “Is it the intervention or the students? Using linear regression to control for student characteristics in undergraduate STEM education research.” CBE-Life Sciences Education 13.1 (2014): 41-48. (Link)

2nd Session

  • Dunlosky, John, et al. “What works, what doesn’t.” Scientific American Mind 24.4 (2013): 46-53. (Link)
  • Nehm, Ross H. “Understanding undergraduates’ problem-solving processes.” Journal of microbiology & biology education 11.2 (2010). (Link)

3rd Session

  • Carpenter, Shana K., et al. “Using spacing to enhance diverse forms of learning: Review of recent research and implications for instruction.” Educational Psychology Review 24.3 (2012): 369-378. (Link)
  • CUNY Office of Academic Affairs, “Best Teaching Practices” (2011) (Link)

 

2016 Spring Sessions Flier

M2

Readings for Fall 2015

 

 

2015 Fall Sessions Flier

STEM-Flier-2015-Fall

Expert and Novice Students; Writing and Active Learning

Facilitators: Daniel Collins, Patrick Lloyd, Kristin Polizzotto

Attending: Jameelah Hegazy (Nursing), Ivan Ho (Viological Sciences), Jen Roman (Biological Sciences), Thomas Greene (Physical Sciences), Martin Litwack (Math and Computer Sciences), Dmitry Brogun (Biological Sciences), Mara Gittleman (KCC Farm), Tara Scannell (Biological Sciences), Farshad Tamari (Biological Sciences), Daniel Collins (Math and Computer Science), Shoshana Bobker (Physical Sciences), Patrick Lloyd (Physical Sciences)

1. Review of First Meeting

2. Expert Students in the Clark Paper

Clark, R.E., Kirschner, P.A., & Sweller, J. 2012. Putting Students on the Path to Learning. American Educator Spring 2012:6-11

Question: Do we have any STEM classes with a preponderance of “expert” students, such that we should switch pedagogical strategies? (Clark makes a distinction between “novice” students and “expert” students and how each learns best.) We certainly have some expert students in cases; e.g., students who already hold B.A.’s (esp. among foreign students). Commonly they will be listening without needing to take notes. While we may not have classes with a majority of such students, we might leverage their expertise by group projects and team work. However, this requires careful assessment, assigning roles, and individual work with connected parts or topics. Some instructors use team work every other class. See also: the KCTL team-based learning FIG.

3. Novice Students and Course Prerequisites

On the other hand, difficulties result from having many “novice” unprepared students in a class – especially because CUNYFirst does not properly verify course prerequisites. This is an endemic problem across Math, Biology, etc. courses. Physical Sciences require both basic reading & math tests to be completed before registering courses, and an office staff member manually verifies all registrations; similar work is now done in the Math office.

Question: What is the value (if any) to the Elementary Algebra prerequisite for most science courses? The primary value may be as a proof of discipline and knowing how to study; the algebraic techniques themselves are certainly used but possibly secondary in importance. Question: Which is more critical the arithmetic (pre-algebra) or the elementary algebra? The abstract-thinking of algebra seems more important; but arithmetic also crucial (e.g., working with decimals, students who have no experience with physical measuring instruments like rulers, decimal mistakes with medication dosages can kill).

Even if prerequisites are taken, wide variation in how different instructors or other schools teach the prior courses can leave gaps or weaknesses. Courses get bogged down needing to re-teach subjects for lack of prerequisites (also changes such as Anatomy & Physiology no longer needing any BIO prerequisite). On the other hand, it’s currently hard to determine requirements for an A.A. degree for advising purposes (esp. whether a lab science course is required).

4. Writing and Active Learning

Question: What is the value of writing requirements on exams such as in Biology? One: It facilitates learning, and reinforcement on tests extends that learning. Two: It simulates and prepares for the experience of writing professional research lab reports. Ideally, students would be writing lab reports as by the middle school grades; exercising the use of math, graphs, etc. Question: Is there any risk of students exercising professional writing but not the complementary reading skills? Most instructors use presentation software (e.g., PowerPoint) in some cases, and students may not be reading them. These skills should be practiced in the earliest courses; don’t wait until later courses.

Commitment should be made to persuading students to be active learners (not just receivers of knowledge). Ideally critical-thinking activities should commence in the 6th-7th grades. In these early grades, differences are seen between specialized science teachers and general education teachers; NYS requires specialists by middle school, but some states still use general education teachers for K-12 (e.g., FLA). One problem with schools of general education is that they may not have rigorous science departments or classes.

5. Next Meeting

Next meeting is Monday, May-18, at 12:40 PM. At that time we will discuss the Alfieri paper, a meta-study on the difference between explicit instruction and discovery learning (for added depth to the Clark/Mighton papers). Minutes to this meeting, and any other articles, will be posted to the wiki as usual.

Alfieri, L., Brooks, P.J., & Aldrich, N.J. 2010. Does Discovery-Based Instruction Enhance Learning? Journal of Educational Psychology 2011, Vol. 103, No. 1, 1-18.

Minutes submitted by Daniel R. Collins

Introduction; Discovery-Based Learning; Use of Textbooks

Facilitators: Daniel Collins, Patrick Lloyd, Kristin Polizzotto

Attending: Grace Axler-DiPerte, Shoshanna Bobker, Dmitry Brogun, Daniel Collins, Christina Colon, Mara Gittleman, Jameelah Hegazy, Ivan Ho, Maria Karfitsas, Martin Litwack, Patrick Lloyd, John Mikalopas, Mary Ortiz, Kristin Polizzotto, Jewel Powell, Jen Rosseau, Tara Scannell, Steven Skinner, Farshad Tamari

1. Introduction of participants

2. Overview of today’s articles

Mighton, J. 2013. For the Love of Math, Scientific American Mind 24:60-67

Clark, R.E., Kirschner, P.A., & Sweller, J. 2012. Putting Students on the Path to Learning. American Educator Spring 2012:6-11

These two articles present somewhat different opinions on the value of direct instruction vs. discovery-based learning in terms of student success. After brief discussion, the group agreed that discovery-based learning is good for small groups, advanced students, and for teaching students how to think (as opposed to teaching basic concepts such as definitions or methodologies & techniques). Direct instruction is best for larger groups, beginning students, and the presentation of new concepts such as definitions, methodologies, and techniques.

3. Personal experiences with these instruction methods

Participants then shared their own impressions of these methods in their teaching at Kingsborough, summarized below:

  • POGIL (process-oriented guided inquiry learning)—some students understood concepts better (more deeply), but most were uncomfortable with this method and really wanted direct instruction

  • A mix of direct instruction followed by practice of the new concepts using discovery-based methods seemed to work best. Examples shared: the unknown microbe riddle (microbiology), figuring out how much of a certain food one must eat to get your RDI (nutrition).

  • Direct instruction helps when students struggle with independent reading. In a nursing class, 80% of the time might be spent on direct instruction, followed by 20% working in groups with each student assigned the role of a specific clinician, and working together to write a treatment plan & rationale.

  • One challenge is to break the topics into smaller steps (modules). Each module may consist of some initial direct instruction followed by practice using some sort of active learning strategy. How can an instructor figure out what these modules should be? One way is to compare various textbooks and see what the consensus seems to be, or use outlines to structure the learning.

  • The question arose as to what is the most effective split of classroom time between direct instruction and discovery-based learning. The group felt that this depended on the assessment methods in the class. If the grades are mainly based on tests of knowledge of concepts, more direct instruction is helpful. If tests focus on problem-solving and how to think, more discovery-based learning is helpful.

4. Use of textbooks

Some discussion ensued as to the value of textbooks in the learning process, including discussion of adaptive technology developed by publishers that has begun to replace textbooks in some cases. Traditional textbooks align with the direct instruction model, while some newer technologies align more closely with discovery-based learning. Math and science are traditionally textbook-driven, but this is changing. Concepts and definitions are often embedded in examples rather than defined in columns of text. While it seems to be true that consumers (students) would prefer not read traditional textbooks, it is less clear at this point whether such adaptive technologies lead to greater student success. This will be an interesting avenue of research in the near future.

5. Synthesis and conclusions

We then discussed how best to integrate direct instruction and discovery-based learning in our classrooms for our particular students. The following comments and suggestions were made:

  • In some way, compel students to read or review concepts before class discussion (such preparation must have points attached to it somehow, or they will not usually do it).

  • Begin the class with questions about previously discussed topics, on which the new tpoics will build.

  • STEM classes of necessity must work at the application level of Bloom’s taxonomy. The knowledge level is critical as a foundation, but there’s never a time in a STEM career when that is enough on its own. So application of concepts must occur at some point in the course.

  • Understanding and application exercises should follow the knowledge stage as soon as possible, immediately when possible.

  • Make concepts “real” to make them stick and be meaningful to students.

6. Next meeting

  • Monday 4/20 12:40-1:40, room TBA (M-391 is not big enough for so many participants)

  • Check the STEM FIG wiki for links to articles (from past and future meetings)

  • Minutes from each meeting will also be posted on the wiki (http://kctlstemfig.pbworks.com)

  • For the next meeting, we plan to discuss articles outlining specific strategies that have been proven successful for STEM students, on the basis of evidence (pedagogical research). Links to these articles will be posted on the wiki, and emailed to participants ahead of time.

Minutes submitted by K. Polizzotto