This is an excerpt from the discussion on the Nature of Science (NOS) from a meeting of the ASU CRESMET Project Pathways group that  Brad is working on. Brad provided the information in this post and the Mathematics and the Nature of Science Definitions posts. The three related posts (including the two following) provide definitions of terms and background for the MCC group discussions in their regular meetings.

 

 

 

A person explores numbers, shapes, etc. and hunts for a pattern. For example, for “fun” one day in his spare time Pythagoras explores the properties of right triangles. He begins with the assumption that some “simple” numerical pattern should hold concerning the length of its sides. He makes this assumption because of his belief that God created the universe, including triangles, and did so using mathematical relationships (i.e., God is a mathematician).

So Pythagoras guesses that perhaps the length of side “a” plus the length of side “b” equals the length of side “c” (call this a conjecture - in science this would be called a descriptive hypothesis) and reasons like this:   

If…true
and…side a = 1 unit and side b = 2 units
then…side c should = 3 units.
But…side c equals about 2.25 units.
Therefore…my conjecture is wrong and I need to try another.

So Pythagoras generates another conjecture (i.e., another descriptive hypothesis).

Perhaps a + b^2 = c.

If…true
and…side a = 1 unit and side b = 2 units
then…side c should = 5 units.
But…as we saw, side c = about 2.25 units.
Therefore…this cannot be correct and I need to keep trying.

And so on, until Pythagoras thinks back to his days as a carpenter building walls. He recalls that when he needed a 900 angle, he first laid boards on the ground. He then took his tape and measured 3 units along one board and marked it. He then measured 4 units along another board to be perpendicular, and marked it. Finally he measured 5 units between the two marks - voila a 3, 4, 5 right triangle with a 900 angle.  [Note that Pythagoras has used the process of abduction to generate this conjecture.]

Pythagoras then notes that 32 + 42 = 52 (i.e., 9 + 16 = 25) and wonders if this will work for other triangles.

So he tries it for several other triangles, e.g.,
If…the square of the sides adjacent to the right angle equals the square of the hypotenuse
and…a = 4 and b = 6
then…c should equal the square root of 52, or about 7.2 units.
And…when he measures c’s length, it turns out to be very close to 7.2 units.
Therefore…he has support for his idea.

Now Pythagoras, convinced that the pattern holds for all right triangles, wonders if he can demonstrate that it does so in a more general way (i.e., he is tired of measuring specific triangles and getting close, but not exact results). So he sets out to demonstrate in a general way that that a2 + b2 = c2.  After much trial and error he hits on the following:

If…a2 + b2 = c2 holds for all right triangles
and…I draw a figure like the one below :

 

then…I should be able to rearrange the parts in some way to show that a2 + b2 = c2 (this is my expectation/prediction).
And…

1) (a + b)2 – c2 = 2ab;  , 2)  a2 + 2ab + b2 – 2ab = c2
3) a2 + b2 = c2 (this is my result). Note that my prediction and my result match perfectly.
Therefore…I conclude that my generalized conjecture is correct (i.e., a2 + b2 does in fact = c2). Let’s call this conclusion a theorem. Let’s also call my demonstration that a2 + b2 does in fact = c2 a “proof.”  

Pythagoras is very happy and excited about his “proof.” So he writes it down step-by-step and shows it to his friends to see what they think. All four of them agree that:

1) Pythagoras is very clever;
2) his steps are convincing that in all right triangles a2 + b2 does indeed = c2;  
3) God really is a mathematician; and
4) math is “beautiful.”

Subsequently, other people hoping to be viewed as clever by their friends (and their enemies as well) also try to generate “proofs” that a2 + b2 = c2. To date at least 45 such proofs have been constructed.

(see www.cut-the-knot.org/phythagoras/index.shtml)

Note that for several reasons the details of this discussion are certainly wrong. Nevertheless, the claim is that math, like science, is a hypothetico-deductive (i.e., If/and/then/but/therefore) enterprise. Consequently, to teach math as math is practiced, we must allow students to generate and test their own mathematical conjectures. Doing so will help them become mathematically literate and “see” for themselves something of the “beauty” of mathematics.  

Note from Mike (from the Project Pathways group):

A hypothesis (in math) is the first part of an implication, i.e., it is the A in the statement "If A then B." The second part, B, is known as the predicate (but that word is not as commonly used). These implications are typically called "theorem," "corollary," "lemma".

A (null) hypothesis (in statistics) is a statement that is tested by developing its implications (If A then B) where B is a probabilitydistribution of possible sample data outcomes. It is rejected if a data outcome is "not likely" (small p value) given that hypothesis. The opposite of the null hypothesis is called the alternative hypothesis, which cannot be tested but only inferred from a rejection of the null.

I see a logical connection to hypothesis in the scientific method, which is a possible explanation for a phenomenon that has not been tested. Like a mathematical hypothesis, one typically tries to develop its implications (If A then B). Like a statistical hypothesis (but unlike a mathematical hypothesis), it is tested by seeing whether the implications (predictions) are consistent with data.

Another meaning of hypothesis in math is synonymous with conjecture, which is an implication that has not been proven or disproven. Typically a proposition is not called a conjecture unless someone has proposed it as likely true.

Note from LD: some of the bold type is from my parsing of the discussion. 
 

 

 

 

These definitions are from Brad's ASU CRESMET Project Pathways group. 

 

The general Nature of Science definitions are in a separate post. 

 

Mathematical Definitions

Mathematics  The exploration of numbers, patterns, and their general relationships.

Where structure involves both elements and transformations/operations with general characteristics such as reversibility, path independence, self regulation, subordinate and super-ordinate relationships. Mathematics includes seeing the same features across diverse examples and often requires abstract formulations (as opposed to concrete, context-dependent descriptions). The endeavor of mathematics is to discover and prove new structural relationships.

Pure Mathematics   The exploration of numbers, patterns, and their general relationships, with no intent to apply results to the real-world. 

Applied Mathematics   The exploration of numbers, patterns, and their general relationships with the intent to apply results to the real world. 

Theorem    A mathematical statement that has been proved (e.g., Aubel’s theorem: Given a quadrilateral, if we draw a square on each side the two lines joining the centers of squares on opposite sides are perpendicular and of equal length. Pythagoras’ theorem: Given a right triangle, the area of the square drawn on the hypotenuse is equal to the sum of the squares drawn on the other two sides. Fermat’s last theorem: If x, y, z, and n are integers, there are no solutions of xn + yn  = zn with n > 2 and x, y, z > 0 ).

Conjecture   A mathematical statement that mathematicians think is probably true but has not yet been proved (e.g., Goldbach’s conjecture: Every even number can be written as the sum of two prime numbers – it is true for every even number that has been checked but it has not ever been proved to be true in general.)

Proof   A step by step argument that presumably shows that a result (i.e., a lemma, a corollary, a theorem) follows from a chosen set of axioms. Whether or not a particular set of steps constitutes a proof is decided by a group of presumably “expert” mathematicians.  

Axioms   Mathematical statements assumed to be true that form the foundation of a field of mathematics. The axioms cannot be proved. The set of axioms must not lead to contradictory conclusions, nor should it be possible to prove one axiom from others in the set (e.g., the fifth of Euclid’s five axioms can be stated as: given a line L and a point P that does not lie in L, there is only one line through P that is parallel to L) (synonyms = postulate, assumption). 

Lemma   A small result that is proved as a stepping stone on the way to the proof of something bigger. In the course of proving a theorem, mathematicians might prove several lemmas.

Corollary   A mathematical statement that follows immediately from another statement without further steps of proof being required – a minor result that is an immediate consequence of a particular major result. 

Statistical hypothesis   A statement about an unknown sample value (e.g., the mean height of a sample of tenth grade students is 5 feet 8 inches; their mean score on a math test is 85%). Statistical hypotheses differ from scientific hypotheses in that scientific hypotheses are creatively derived as possible causes of puzzling observations. Suppose for example that a teacher found that the mean score on a math test of tenth grade females was twice as high as that of tenth grade males. To explain this puzzling observation, the teacher advanced the scientific hypothesis that the observed difference was due to the fact that all of the test questions were embedded in feminine contexts. 

Null hypothesis   A statistical hypothesis to be tested and accepted or rejected in favor of an alternative. For example, a null hypothesis proposes that the observed difference between the means of two samples is due to chance alone and not due to a systemic cause. Thus rejection of the null hypothesis implies that the observed difference is not due to chance.  

In hypothesis testing, a prediction based on a statistical test of a scientific hypothesis being tested assuming that the hypothesis is false. Mathematicians have Ho (the null hypothesis) and H1 (the alternative hypothesis). If the statistic falls within some region, called the region of acceptance, they accept Ho. Otherwise they reject Ho and accept H1.    
The null hypothesis is not a prediction. The test distribution is the prediction. The null hypothesis is used to generate this prediction. See my previous email on this.

 

(null) hypothesis (in statistics) is a statement that is tested by developing its implications (If A then B) where B is a probability distribution of possible sample data outcomes. It is rejected if a data outcome is "not likely" (small p value) given that hypothesis. The opposite of the null hypothesis is called the alternative hypothesis, which cannot be tested but only inferred from a rejection of the null.

Mathematical Model   A type of model (i.e., representation) that specifies mathematical relationships presumably similar to those in a real situation so that when mathematicians solve problems within the model system, their solutions can be applied to the real situation. There is reality. Then there is a simplified (idealized) version of reality that selects certain things to attend to, certain things to ignore, and certain simplifications. This is not yet a mathematical model. Elements of a mathematical model correspond to elements of the idealized model that have mathematical relationships that reflect relationships in the simplified model.

Parameter  A variable that becomes a constant in particular situations (e.g., half-life for carbon dating is a constant – a parameter, while other variables, such as the proportion of C14 to C12 varies. Across other isotopes half-life varies. Parameters are important in function models where they are not the independent or dependent variables. For example, in the standard interpretation of y = mx + b as the equation of a line with y as a function of x, m (slope) and b (y-intercept) are parameters. They are constant for a given line in which x varies and y varies. But they may vary to describe other lines. In statistical models, the parameters are fixed values related to a population, e.g., mean and standard deviation are treated as constants). 

This post contains information from the attachment Brad sent the MCC group on 9/2/05. These are definitions of terms from discussions of the ASU CRESMET Project Pathways participants, including Brad. Mangala and Dave are also involved in other parts of the project.

 

The mathematical terms are in a separate post.

 

 

Building a Dictionary of Key Nature of Science and Mathematics Terms

Nature of Science Terms

1. test
2. induction
3. abduction
4. postulate
5. fact
6. nature – natural phenomena
7. supernatural vs. natural causes
8. replication
9. uncertainty
10. Occam’s razor

analogy  An agreement, likeness, similarity, or correspondence between the relations of things to one another; a form of reasoning (analogical reasoning) in which such similarities serve as a source of hypotheses.

applied research  Research aimed at answering questions that have practical human applications, e.g., determining the causes of diseases so that cures might be found.

assumption    Something taken for granted; act of taking for granted; a supposition. Note: Assumptions may not be correct.

basic research   Research designed to describe or explain nature to satisfy one's curiosity.

bias  A pre-established tendency or inclination in favor of one explanation, belief, idea, that prevents unprejudiced consideration of alternatives.

circumstantial evidence  Evidence that tests an explanation by observing  other events or circumstances that according to common experience are usually linked to the cause (e.g., a wet street is usually caused by rain, therefore seeing a wet street in the morning supports the hypothesis that the pitter patter you heard on your roof last night was caused by rain). However, circumstantial evidence does not necessarily rule out alternatives (e.g., a burst fire hydrant may have sprayed the street).

concept  A mental construction (i.e., an invention) representing a real and/or only imagined object, event or situation plus the associated term; a mental picture; an idea; a notion.

conceptual system  A group of related concepts that derive meaning from one another and from analogies.

comparison group   Individuals in an experiment that either differ from the experimental group individuals in only one way, or are treated differently than the experimental group individuals in only one way; used as a comparison with the experimental group; sometimes called the control group.

conclusion  A statement, or statements, that summarize the extent to which hypotheses have been supported or not supported.

constant  A characteristic (property, trait) with values (e.g., numbers, colors, sizes) that do not differ from one object, event, or situation in a group to the others; e.g., in a group of students, they all have one nose, thus "number of noses" is a constant.

controlled experiment  A "fair" test. An experiment in which the values of only one independent variable differ; the values of other independent variables are the same, they are held constant or "controlled."  

correlation   Mutual or co-relation of two or more things, parts, variables. 

correlational evidence   Evidence that tests a possible explanation by determining the extent to which the values of two or more variables, which have been predicted to be correlated, are in fact correlated.

deduction  An If/and/then pattern of reasoning in which an assumed to be correct statement and an imagined test condition together allow the derivation of an expected (i.e., potentially observable) consequence.  

dependent variable  The outcome variable, the effect; the response; the variable in an experiment whose values vary in response to changes in the values of the independent variable; in mathematics f(x) denotes a dependent variable, i.e., a variable such as y, whose values depend on the values and relationships among one or more independent variables. 

descriptive question  A question inquiring into the who, what, when, where, but not why, of some observed object, event or situation; e.g., What types of vegetation changes occur as one travels from Michigan to Arizona? When did Kris's family travel up Mt. Lemmon?  Where are the Catalina Mountains?

disprove  To establish as false beyond any possible doubt.

experiment  A manipulation of nature designed to test a tentative explanation, a hypothesis, a possible cause.

experimental evidence Evidence derived from an experiment that tests tentative explanations/hypotheses/causes.

experimental group   Individuals in an experiment that either differ from the control group individuals in only one way, or are treated differently than the control group individuals in only one way.

emergent properties   Unique properties of nonliving objects or of organisms that arise as a consequence of novel arrangements of parts.  Emergent properties of organisms arise during their evolutionary, embryological and intellectual development.causal question   A question inquiring into the cause or causes of some phenomenon; e.g., Why does vegetation change from place to place? Why is it hotter in Arizona than in Michigan? Why is it cooler at the top of mountains than at the bottom? How can it snow in Arizona? 

hypothesis  (plural, hypotheses) A statement intended to explain a  phenomenon; a possible cause for a specific puzzling observation.

independent variable  The input, manipulated, or causal variable; the stimulus; the variable in a controlled experiment whose values vary to see if that variation causes a change in the outcome of the experiment.

law  A statement that summarizes a pattern of regularity detected in nature i.e., the manner or order in which a set of natural phenomena occur under certain conditions. A satisfactory explanation for the detected pattern may not exist.

model  A representation, generally in miniature, to show the structure or serve as copy of something.

observed result  The outcome of a test, evidence, data, to be compared with an expected/predicted result.

planned test  Imagined conditions that when carried out test a hypothesis.

prediction  A statement of an expected (future) outcome of a planned test assuming that the hypothesis being tested is correct; to be compared with observed result to test the hypothesis.

prove   To establish as true beyond any possible doubt.

theory  A collection of statements (conditions, components, claims, postulates, propositions) that when taken together attempt to explain a broad class of related phenomena.

value  A specific quantity, magnitude, number or rank of a variable or system of classification (e.g., among people, values of the gender variable are male and female; values for the weight variable are 100 lbs, 150lb s, and so on).  

variable  A characteristic (property, trait) with values (e.g., numbers, colors, sizes) that differ from one object, event, or situation in a group to the others; e.g., in a group of students, their heights differ, thus "height" is a variable characteristic, a variable; Opposite of constant.

I started this in my blogger account that I was trying out, but I decided to start fresh, just like our group. This is a place to review what we have done and what we are supposed to be doing. 

 

For general information about the leadership initiative we are affiliating with, go to www.pkal.org. 

 

I'm going to try to chronicle our journey. I have to decide whether to make this more personal, or more general. Brad will have to decide whether to start a blog or some kind of official communication for the group.

 

LD

 

Here are the significant email communications to and from Brad so far (reverse chronological order). This provides both a historical record and a reminder of what needs to be done. I have only edited out meaningless chit-chat. :-)

 

9/2/05

To: dl-stemflc@mail.mc.maricopa.edu
From: kincaid@mail.mc.maricopa.edu

Hello all,

Our preparation for the KC trip gives us some motivation to begin our discussions in earnest. I propose that we begin work on two opportunities related to the KC meeting.

• Prepare a poster stating the problem, rationale objectives of our work.

Notice in the KC agenda that "Participants are invited to present a poster that documents a personal experience in designing courses, programs, spaces, budgets, etc. that support one or more specific goal(s) for student learning." This is an opportunity to share our ideas and get feedback from others. It is also motivation to get focused on what we hope to accomplish. It does not have to be very sophisticated. It could even be a list of questions for discussion/feedback.

• Design a conference session on NOS.

If we could attend a session to inform us and others about the nature of science, why students should learn about it, and how we should teach it, who would we invite and how would we organize it? We actually have that opportunity. Through my role on the planning committee for PKAL's national assembly in Chicago next spring, we can accomplish this. PKAL has a way of getting national leaders to respond to invitations for participation, so we would have a shot at getting anyone. So who are the national leaders in NOS, who would we invite, and what would we want them to do?

For our next meeting, we need to thinking about the Nature of Science, Math and Technology (NOS). What is it that we want students to know and why is it important? I propose that we search through our references and find the best ones regarding NOS. I propose that we develop a ranked and annotated bibliography for NOS (as well as for every topic that we discuss). We need to start developing a common vocabulary for us and our students. I have attached a draft of a list generated by the ASU group I'm working with. Compare these to the usage in many of our textbooks and you start to get a sense of the problem. Do any of you have any great examples of the misuse of these terms?

So for Thursday, can we each:

• Bring a short list of references. And for each, you might develop a rationale for why the rest of us should read it. We will figure out how to collate our lists electronically later.
• See what you think of the ASU NOS vocabulary list.
• Think about the opportunities described above.

Brad

9/2/05

Hello all,
 
Here are some details regarding our travel.  The Agenda has been posted at http://www.pkal.org/template2.cfm?c_id=1528  Regular sessions at the colloquium begin at 3 pm on Friday and end at noon on Sunday.  We will each pay our expenses and get reimbursement upon return.  If that is a problem for anyone, let me know and I will make other arrangements for you.  Remember to KEEP ALL ORIGINAL RECEIPTS.

    •     Everyone traveling must complete a travel acknowledgement form EACH year.  It is attached for your convenience.  Simply complete the form in MS Word, sign and turn in to the Fiscal Office.
    •     I hope everyone will arrange for a sub for Friday.  I would be happy to talk to your chair if there is any problem.  This is not like a standard conference.  We will participate as a group and usually do some group activities. 
    •     Make your hotel reservation using info from http://pkal.org/template2.cfm?c_id=1529 
    •     Make your airline reservations.  America West is cheapest at $242.  (See below)  Lowest Southwest flight is $314.  AWA has a good nonstop leaving at 9 a.m. with a 2:40 return on Sunday.  SW has a 6:15 am flight with  3:20 and 9:40 returns.
    •     Everyone must complete a travel request form.  It would be best if I turn all these in to Donna together, so she knows what account number to use.  Your department should have a supply of them.  Request airfare, taxi/shuttle and lodging -- PKAL always provides great food.  Enter $150 per night for the hotel because the quoted rates don't always include all taxes.  Enter an amount for shuttle or taxi to and from the airport (sharing a taxi may be the cheapest if we travel together).
    •     I will register us all with PKAL as a group, so you do not need to fill out the registration form.
    •     Upon return, fill out a travel reimbursement claim with original receipts showing the balance paid attached.  Turn them in to the cashiers office.  Reimbursement checks are usually pretty quick because everything is preapproved.
I am participating in the PKAL Chicago planning meetings, so I will go early and leave a little later (probably the SW flights).
 
We cannot delay in making reservations, as fares can go up.  We can fill out travel reqs in our next meeting.  Let me know if I have not answered any quesitons or if anything needs clarification.
 
Brad
 
The list of attendees I have is below.  Let me know if I have missed anyone.
Brad Kincaid
Liz Dorland
Mangala Joshua
Madeleine Chowdhury
Peter Brown
Paul Nunez
Niccole Cerveny
Ly Tran-Nguyen
 
AWA:
 
Depart Arrive Flight # Details 9:07 AM 30 Sep 2005
Phoenix, AZ 1:48 PM 30 Sep 2005
Kansas City, MO
590
Travel Time 2 h 41 m 2:40 PM  02 Oct 2005
Kansas City, MO  3:31 PM 02 Oct 2005
Phoenix, AZ
623
 
SW:
 
Depart   Sep 30 Fri N/S PHX-MCI  542 Depart Phoenix (PHX) at 6:15 AM
Arrive in Kansas City (MCI) at 10:55 AM  
Return   Oct 02 Sun N/S MCI-PHX  1479 Depart Kansas City (MCI) at 3:20 PM
Arrive in Phoenix (PHX) at 4:10 PM
OR
Return   Oct 02 Sun N/S MCI-PHX  671 Depart Kansas City (MCI) at 9:40 PM
Arrive in Phoenix (PHX) at 10:25 PM 

 

 

 

Hi Derek and Niccole (and Adam, Amadou and Paul, see below), 

I am writing to invite you two to join a group that we are forming at MCC to tackle an issue in science education.  For us, 'science' refers to all the traditional science, technology, engineering and math disciplines as well as all others that use a scientific approach.  You can see the other members and some general background information from the attached email.  You can see that this is a great group!  Basically, the idea is for us to form a faculty learning community to address the general question "what is the nature of science and how should we teach it?"
 
We met for the first time last Friday and you two were nominated to join us.  Originally, we planned to meet n Friday afternoons, but several people had problems with that time.  You can imagine the difficulty getting a group like this together at one time.  So now, we are planning to try a bimonthly meeting on Thursday evenings from 5-7.
 
In addition, we have funding to travel to some Project Kaleidoscope conferences (www.pkal.org).  The first meeting we are planning to attend is Sept. 30-Oct 2 in Kansas City.  And you will get $1,000 honorarium in recognition of your valued contributions.
 
I'm sure you have many questions.  I will try to contact you Monday at school.  It would help me if you could reply with times you would be in your office, so I can call.  You can also reply all to this group to ask questions or make comments.
 
This link will take you to a first draft of our application to be part of the PKAL STEM Leadership Initiative that is described in the brochure at the next link.

http://www.mc.maricopa.edu/~kincaid/public/PKALNaturalScienceCommunity3.pdf
http://www.pkal.org/documents/2005_PKAL_LI_Brochure.pdf
 
And this is a link to an essay that I wrote about CC involvement in overall movement to improve undergraduate STEM education.  I promised to send it out to all the group, so here it is...

http://www.mc.maricopa.edu/~kincaid/public/BringCommunityCollegestotheTable6.pdf
 
Thanks, Brad
 
PS: Adam, Amadou and Paul, does Thursday evening work (5-7) any better for any of you?  We are really hoping that at least one of you will be able to join us.

 

 From:       kincaid@mail.mc.maricopa.edu
    Subject:     FW: PKAL Leadership Initiative
    Date:     August 9, 2005 7:55:59 PM MST
    To:       liz.dorland@mcmail.maricopa.edu, mjoshua@mail.mc.maricopa.edu

 

Hi,
 
I received this regarding our idea to get support for our discussion group from PKAL.  According to Jeanne, this is really a flexible program, so it could cover what we want to do (I think).  Here is info about the program.  

 

http://www.pkal.org/documents/2005_PKAL_LI_Brochure.pdf
 
I was thinking that we might try to organize around the FLC (faculty learning community) principles as much as possible.  At least, let's talk about it.  You can see more at  http://www.units.muohio.edu/flc/
 
As soon as possible, we need to get our ideas together, so we (or I) can approach Gail and Carol for support.  We will need a set aside for some travel money for each of the core group.  I will also propose that each of the core group be nominated as PKAL F21, which will also include continued support for travel to a PKAL Assembly.
 
Who is our core group besides us?  Madeleine?
 
Brad

 

From: Jennifer Luebbert [mailto:jluebbert@pkal.org]
Sent: Wednesday, August 03, 2005 10:58 AM
To: kincaid@mail.mc.maricopa.edu
Subject: PKAL Leadership Initiative

August 3, 2005

W. Bradley Kincaid
Professor & Chair of Life Science
Mesa Community College

Dear Brad:
Greetings. We were pleased to learn of your interest in becoming a PKAL Leadership Institution, and look forward to your completed application. We are assembling materials that will be sent out as the final application is received.

One essay in the packet to be distributed is "The Tasks of Leadership" by John Gardner (published with permission).

+ http://www.pkal.org/open.cfm?d_id=516

As an introductory step for your team, we ask that you meet and discuss this essay , and send one collective reflection back to the PKAL National Office by mid-September.

Please note the upcoming seminars for PKAL LI institutions. You can find more information on these seminars at:

Leadership in Building Research-rich Learning Environments
+ http://www.pkal.org/template2.cfm?c_id=1534
Leadership in Building Interdisciplinary Programs
+ http://www.pkal.org/template2.cfm?c_id=1533
Leadership in Building Programs that Ensure the Success of All Students
+ http://www.pkal.org/template2.cfm?c_id=1541

The expectation is that each LI team participate in at least one of the seminars each year. They begin with breakfast on the opening Friday and end at noon on Sunday (plan travel accordingly). There are pre-seminar assignments (such as the Gardner essay); each team is to leave the seminar with an amended statement of vision, goal, strategies and action, building on their application. During the academic year, PKAL will provide targeted assistance to each campus, appropriate to individual needs.

Also, please note the 2005 PKAL National Colloquium: Translating How People Learn into a Roadmap for Institutional Transformation.

+ http://www.pkal.org/template2.cfm?c_id=1525

We believe this is the first-time ever to bring cognitive scientists, STEM faculty, design professionals, and other leaders together to talk about the implications of insights about "how people learn" to the work of transforming the undergraduate STEM learning environment. We hope at least one member of each LI team joins us for the colloquium, perhaps with an administrator responsible for academic planning.

We look forward to our collaborations in the coming years. In 2007, there will be two national meetings disseminating what we've learned- within PKAL and on individual LI campuses- about the work of institutional transformation.

Be in touch if you have questions.
- Jeanne L. Narum & the PKAL National Office

 

 

From:       kincaid@mail.mc.maricopa.edu
    Subject:     RE: NOS and labs
    Date:     August 9, 2005 7:34:14 PM MST
    To:       liz.dorland@mcmail.maricopa.edu

 

Hi Liz,

I am around now for what is left of the summer.  It would be good to have
lunch and talk.  I just got back from Mexico, so I'm still decompressing a
bit.

I did hear from Jeanne about the PKAL leadership institution application.
She is very supportive and in fact spoke to Gail about it when she was in
DC.  We will need to get a core group together to make the application and
decide on the focus of our group.  I did some reading about faculty learning
communities and one of the many keys to success is to have some common goal
to work on.  It seems that it should be something fairly straight forward
that we can all relate to.  There are many other ideas at

http://www.units.muohio.edu/flc/

If we get organized and get some admin support, we should get a group ready
to go to the PKAL National Colloquium:

 

Translating How People Learn into Roadmap for Institutional Transformation

Kansas City Marriott Country Club Plaza & the Stowers Institute for Medical Research

Kansas City, Missouri
September 30 - October 2, 2005 

 

The 2005 PKAL National Colloquium will be an opportunity to envision the college

or university of the future that takes student learning seriously, from the perspective

of research on "how people learn."  Sounds good to me!
BTW, it occurs to me that Dennis Wilson is really interested in your topic
too.  He is on the path of having students produce the multimedia to really
engage them in the topic and give them (make them take) responsibility for
their learning.  Interesting topic.

I still have not talked to Gail yet, but think your idea about the CTL was
correct.  I will listen, but...

 

I have made committements to ASU, PKAL

and our group that I am really dedicated to pursuing.

Let me know when you want to get together.

Brad


-----Original Message-----
From: Liz Dorland [mailto:liz.dorland@mcmail.maricopa.edu]
Sent: Tuesday, August 09, 2005 7:06 PM
To: Kincaid Brad
Subject: NOS and labs

Hey Brad,

I'm still working on the research phase of my literature review paper on the
cognitive theories used by producers of animations and multimedia for
college chemistry. I've learned a lot of cool new stuff and found a lot of
references.

Here is an NAS-NRC workshop that you might find interesting because of the
NOS focus even though it was last year and mainly about high school labs.
Some familiar names there, and the speakers generated individual reports
(linked on the agenda page) as well as a final report document with an
executive summary. Was BOSE the sponsor of the workshop you attended too?

http://www7.nationalacademies.org/bose/June_3-4_2004_High_School_Labs_Meeting_Agenda.html

America's Lab Report: Investigations in High School Science  (2005)
http://www.nap.edu/books/0309096715/html/

http://www.nationalacademies.org/   (note the latest news, including this report)

When do you want to do lunch to talk about our faculty discussion group? I'm
psyched to have some people to bounce ideas off of regularly. I'm around
this week, or we could look at accountability week. I'd like to get a core
faculty group together to talk about it next week before everyone gets too
busy. Maybe we could tie it in with the PKAL national meeting concept and
get some of our faculty to attend.

Cheers!

Liz D.