Learning+Discussion+on+NSTA+Pedagogy+Listserve

Think of this as a blog entry on a particular topic -- concept first vs. rote memorization.

=Working Memory= Dan and Scott -- I'm reading Richard E. Nisbett's "Intelligence and How to Get It." I couldn't help but chime in too. In addition to the long-term memory point Scott makes below, Nisbett's book has me thinking about working memory too. We are only able to hold a certain amount of items in working memory. In order to learn a higher level concept it would seem to me that if prerequisite knowledge for the concept (vocabulary, formulas, or facts) were not already crystallized into longer-term memory, it would be difficult to juggle all the necessary pieces to understand a more difficult concept. Of course what comes first -- the term or the concept might be different depending on the level of the student.

For example, if you look at the Atlas of Science Literacy page 55 when talking about Atoms and Molecules, we should start defining Atoms before the term is introduced by talking about magnifiers and that things are made of parts in K-2nd grade. Then in 3-5 the idea that you can't see something that still exists, but you can if you look through a microscope, is a novel concept. In 6-8 all matter is made of atoms. And from there you can go on to talk about electricity and charges, chemical bonding, etc. Without a thorough grasp of the atom, it may difficult to learn more. The vocabulary word "atom" has a lot attached to it and can grow as you learn more, but that vocabulary word is a helpful hook on which to grow other knowledge.

Rick Winter, Principal, Georgetown Community School,, sent 6/19/09

=Long-Term Memory= On Behalf Of dan@danbranan.com, Sent: Friday, June 19, 2009 6:58 AM, To: pedagogy@list.nsta.org; chemistry@list.nsta.org

Scott, I believe that part of this argument is semantic. When you talk about "learning in context" vs. "memorization", there is really no difference there. If you truly learn a concept (or term or equation, etc.) and by that I mean that you are able to recall both the concept and it's contextual meaning, then you have placed it in long-term memory. In other words, you have memorized it. I think the distinction you may mean to make is between rote memorization and active-learning/contextual-learning methods. The main difference is the means by which the concept is memorized, and one may be more effective than the other in certain circumstances. The second point I'd like to make is that the vocabulary, et al., is just as important for the students as for the instructor. Learning research has conclusively shown these three things in regard to knowledge: 1) The more things you know (have in long term memory) the more things you can learn. To a certain degree, it may not even matter if the existing knowledge and the new material have anything directly in common. The act of learning and being able to recall knowledge expands the brain's ability to learn. As you pointed out, you have the ability to teach yourself new material. To a large extent, that is because you have already learned a large amount of material. 2) The ability to conceive of abstract concepts is directly tied to a person's vocabulary. If you don't know the word for something, you can't adequately shape the abstract concept that is represented by that word in your mind. If you don't have a word for "molecule" in your vocabulary, you cannot adequately conceive of the concept of molecules, for example. 3) The ability to contextualize information is directly related to the ability to recall the information. In other words, to have it memorized. The more often students are required to recall a given fact, the more rapidly they can contextualize it and understand it. I'm currently on vacation, and don't have a ready literature references for you, but I can send them later. Although, the first and third of these ideas are addressed in Willingham's book. Finally, I believe you are confusing the related ideas of information and knowledge. Just as a pile of data is not information until it is analyzed, a pile of information is not knowledge until it is contextualized in long-term memory. The evidence of this, as you say, is the ability to both recall the information and explain it. If students are not required to recall the information, however, they will not be able to contextualize it effectively. The examples given by others on this list about language and mathematics are valid and illustrate what I mean by this.

Dr. Dan Branan Assistant Professor of Chemistry, USAF Academy, CO, Check out my website at: [|www.mini-labs.org] =Calculators= Regarding calculators, let me expand on why they are also dangerous to the future of our nation. (from pedagogy-request@list.nsta.org; on behalf of; Scott Orshan [sdorshan@aol.com] 6/10/09)
 * Students come into my physics class as juniors, after taking Chemistry.
 * They are in Pre-calc. Despite this, they still don't know how to use their calculators.
 * To them, numbers are button pushes. Numbers do not represent quantities or proportions. Arithmetic operations have no meaning. Multiplication, division, exponentiation - those are all just button pushes. Trig functions - they have nothing to do with triangles - they are just button pushes. 5+7, 5*7, sin(5) + cos(7), 5^7 have no numerical meaning.
 * They are just button pushes. And if that weren't bad enough, they don't even know how to push the buttons properly. They learned a rote algorithm for solving a particular type of problem, but since there is no mathematical understanding, they can not solve a new type of mathematical problem.
 * Scientific notation is of particular difficulty. I don't know how they got through Chem. They try to use ordinary exponentiation to enter sci. notation. This sometimes works, but falls apart when the quantity is in the denominator, is squared, or both. There is no sense of size. 9*10^9 and 1.6*10^-19 are just button pushes, not very large and very small numbers.
 * Fractions are not numbers to them. If they think of a fraction as a proportion, then they can not then think of it as a number.
 * To them, 1/2 of x is not the same as x/2. To take 1/2 of something, they will punch 1 / 2 * x. There is no realization that x is a number on the number line, and x/2 is halfway there.
 * Since they have no number sense, they have no idea if an answer is wrong. They put down the most ridiculous answers. Cars have masses of 10^15 kg. The number doesn't mean a thing.
 * Why is this the case? Because starting in elementary school, calculators have replaced manual number manipulation. They might learn an important mathematical principle, but it is then followed by "and this is how you punch it into your calculator." Then they do that 20 times, and feel that they know math.
 * My students have the most trouble with the math that they should have learned in 6th and 7th grade. Fractions, proportions, exponents, percentages, decimals - these are the basis for all of the formulas we use, as well as for dimensional analysis.
 * Definitely at the beginning of the year, but even still at the end of the year some students have difficulty distinguishing "times two" from "squared". 5^2 is 10. x^2 is 2*x. How do you get rid of the exponent?
 * Divide by 2. Why? No meaning to the math - just button pushes.

Biology slant to calculator question
From: pedagogy-request@list.nsta.org [mailto:pedagogy-request@list.nsta.org] On Behalf Of Andrew Petto Sent: Friday, June 19, 2009 9:39 AM

Seriously, I see similar issues in biology that Scott does in chem (and saw them also when I taught Chem and Physics to 10/11/12 students earlier in my career. The numbers and the operations are "pure" --- entities in an of themselves. My chem student would always be amazed when I put up a problem on the board, scanned it for a few seconds and said (without using a calculator or writing down any numbers), "Okay, we are looking for an answer around 10,000." When the answer turned out to be 9775, they were even more amazed. It was, as Scott pointed out, a lack of appreciation for the fact that the numbers and formulae represented some underlying relationship; understanding the relationship is essential to knowing whether the answer is correct or not. In my anatomy courses, the problems that trip up most students revolve around mathematical representations of anatomical relationships --- for example, mechanical advantage of muscles. For example, I ask them how to increase the MA of the biceps (which has a pretty low MA); over half will say to build more muscle and make the biceps stronger, even though we have defined, illustrated, jumped up and down, and so on that MA is a ratio of the length of body segments that does not depend on the force applied to the segment. If none of these segments changes, then MA is still the same. We worked several examples in class. So, clearly we have some work to do (in conjunction with the math teachers?) to find ways of breaking through this. I am not sure we did any better at this age --- and I am not sure our education (or at least mine) was any better at making these connections. But I do remember 2 or three teachers in high school, college, and graduate school who stand out because they made it a point of having us look at these things.

Calculators - Requirements to recall vocabulary, etc.
From: pedagogy-request@list.nsta.org [mailto:pedagogy-request@list.nsta.org] On Behalf Of dan@danbranan.com Sent: Friday, June 19, 2009 10:00 AM

Thank you for eloquently making my case for me, in the context of your well-state case about calculators. The problem of course (and I completely agree with your argument) is that students have not been held accountable for the repeated recall of fundamental mathematical relationships and concepts. If they had, they would be able to relate to the math in a more personal way, instead of by proxy through their calculators.

This will be the legacy of our instructional system in all of the sciences if we don't do a better job of requiring students to learn fundamental relationships, vocabulary, etc. and recall them for use on a regular basis. And yes, this is definitely a danger to the future of our nation. Dr. Dan Branan, Assistant Professor of Chemistry, USAF Academy, CO

Number of facts, vocabulary words
One of the problems is that there are //so many// vocabulary words. There are versions of courses that focus on the vocabulary somewhat to the exclusion of the context in which it's useful -- sort of like teaching Spanish by asking students first to memorize all the nouns, then all the verbs, then the rules of grammar...but not actually having conversations. I did my PhD thesis on a project using Drosophila polytene chromosomes. I knew I'd need to be able to recognize every band on every chromosome, so I spent a couple of weeks at the microscope memorizing them. Then I did the first experiment, which required identifying a particular band to determine if I could proceed with the procedure. This had to be done within 5 minutes. [I know, it's weird, but it made sense then.] I discovered that all my "memorizing" had been for naught. I couldn't do it. But after only 2 days in which I //had// to do it for an actual reason, I learned it. Having a reason and a context made the difference. I suggest that this is quite analogous to the vocabulary problem. It's //hard// to understand the vocabulary if it's not used in context, and in a project that makes students actually care about it. My graduate assistants in the freshman biology lab, when I taught it, often insisted that the way to start the transcription/translation discussion was to go through all of the vocabulary first. Then, when students were doing the lab, they'd have it all in hand. It didn't work. They couldn't put the pieces together. There was no context through which to link the words properly. In my current course, I've taken to talking about the relevant processes, using English, and bring in the Science Words only when we've got a bit more of the relevant picture. Then I freely use the words in their appropriate places...thinking that //using// the terminology is the best way to learn how to use the terminology. There is, of course, one Serious Problem. Maybe not a "problem" but at least a fact of life. For the complicated things, we kinda have to know the terminology to understand the concepts, but we kinda have to understand the concepts to make sense of the terminology. We are probably not at the appropriate place in the balancing act here. To get there, we need more time to spend on the topics...which gets us to the perennial debate over what topics should really be in the course. It helps to remember that most of us didn't "get it" the first time through a lot of the stuff we teach, so it might not be a particularly sound expectation that our students should. --Jose
 * From: ** pedagogy-request@list.nsta.org [mailto:pedagogy-request@list.nsta.org] **On Behalf Of** Jose Bonner
 * Sent:** Friday, June 19, 2009 10:31 AM