It is amazing for what kind of an interesting research people spend money and time.
In Journal for Research in Mathematics education (Volume 36, Number 1, January 2005) I have read a big publication “Children’s Use of the Reference Point Strategy for Measurement Estimation” (I highly recommend you to read it).
I will use my own words (that means, my own understanding of the publication) to describe the main idea of the research and what I think about it.
The researches were comparing two teaching strategies which result in developing children’ skills to estimate a size of different objects, for example to estimate the length of the 9-inch long piece of rope.
The first teaching strategy called the Reference Point strategy was used in the first class of third grade students. The second teaching strategy called Guess-and-Check Procedure was used in another class.
The first result of the research is: “approximately two thirds of students (64 %) who had received the (Reference Point – added by me, but it is clear from the context) strategy instruction used a reference point to estimate … the objects in the posttest interviews”. And only “14 % of those students who were instructed to guess and check also made use of the reference point strategy”. The authors are writing, “… We were successful at increasing the use of the reference point strategy through the strategy instruction we provided”.
This is a really big conclusion! I can translate this result in this way.
If students were taught by a teacher for using of some strategy, the students have a tendency to demonstrate the use of that strategy in the exercises. But if a teacher did not teach students to some strategy, they rarely demonstrate the using of that strategy.
Even simpler we can say, when a teacher teaches students how to do something, the students in general can demonstrate the skills learned, when doing some exercises.
You may think it is an obvious idea; all the education is based on it! Yes, I agree. But, thanks to the researchers, we can convince ourselves one more time in the truthfulness of this rule.
Besides, we can use this rule more effectively if we will read it backwards. We can say that, when students do not demonstrate the use of a strategy, hence the teacher did not teach them how to use that strategy. I mean, maybe the teacher have been doing something like talking to the students, writing on a blackboard, etc, but we cannot say that it was a teaching. It was some kind of activity, definitely, but it was not a teaching (a good way to measure a quality of teacher’s work, isn’t?).
Further we can find one more and even more important result or the research: “…the use of the reference point strategy was statistically associated with greater estimation accuracy”, etc. In other words, the reference point strategy leads to better educational results then Guess-and-Check Procedure (I pity to the students of the second class). Why the first strategy was more efficient then the second one? Do we really need to make some research to find out what strategy would be better then another? The answer is in the description of the strategies.
When you read the description of the strategies it becomes clearly that the students of the first class have been making/proceeding many more learning activities relatively to the students of the second class. Even more, the type of some activities was significantly different. For example “… the reference point group received explicit instruction on referents points – imagining them, iterating reference points across objects both physically and mentally, … The guess-and-check, on the other hand, was simply asked to guess and check the measurements… They did not practice imaging or iterating representations of … inch-long objects…”
We can see, hence, the significant deference in a number and (that is even more important) in a variety of learning activities, which have been undertaken by the students of the two classes.
It is obvious, if I make 10 exercises and you make 100 the same exercises, you will be more trained then me.
It is obvious, if I make 10 (ten) exercises and you make 10 (ten) but more difficult exercises, you will be more trained then me.
Now, combine these two teaching rules and ask yourself, do we really need to do a research to prove the rules?
We can say with sure, that the level of the development of the skills learned by students is directly proportional to the number and variety activities in which the students were involved. This is the direct consequence from the fact, that kids can learn only the activities, which they can proceed/repeat together with adults being involved in some mutual “business”.
The students from the first class have been using (manipulating of) many different objects to train their skills. The students from the first class have been taught to broader variety of ways of using the objects (as the reference point). Of course they have better skills then the students from the second class.
But here I want to emphasize that the students from the first class have been doing many more mental exercises then the students from the second class. Hence, together with more skills developed through the lessons they have had a more developed brain (you know, I consider this educational result as the most important result of elementary education).
Now I have the question, what kind of positive outcomes can we obtain from the research described in the publication?
Let’s repeat once again the fundamental law of teaching: to get students trained/educated, they have to be taught (not trained/educated students have not been taught).
Secondly, the level of the development of the skills trained is directly proportional to the number and variety activities in which students were involved.
The first two conclusions lead to the third one, i.e. a good teacher can organize a large number of different learning activities for the students.
I want to say, that thanks to the research, kids form both classes have met a good teacher (“she had participated in a 5-year professional development program… etc”). At least during the six 45-minute lessons the kids have been doing something more then merely “seatwork and exercises on mathematical procedures”. I believe that now, after the research, the regular teachers work differently, and this is a positive outcome of the research as well. And I believe that such a kind of outcomes is the most important result for any educational research undertaken these days, even if form the point of view of theoretical conclusions the conclusions are obvious*.
* P.S. As a person who
has a good physics education I wonder sometimes on educational psychologists.
After the Sir Isaac Newton we have in Physics three fundamental laws, which
allow us to get derived lots of particular consequences. Today it would be just
a loosing of time if somebody undertook research on measuring the
relationships/dependence between masses, velocities and angles of colliding
billiard balls. Any possible relationships for this situation we can derive
But psychologists keep demonstrating before-Newton’s methodology of making researches. They want to investigate each and every single possible particular event/action/situation instead to derive the results from some fundamental psycho–physiological principles, like “exercises make cells/muscles more developed”. Maybe they just cannot formulate those fundamental principles?
** P.P.S. There is a simple for understanding but far leading fundamental principle, that it, one of the strongest properties of any biological system is a property to support the own life. This property governs the functioning of a system throughout all the living cycles of the system. There are rarely exceptions from this “rule of life”, but those exceptional systems usually do not have a long life because of their self-destroying tendency. Simply speaking, every biological system including human beings wants to be alive as long as it possible. But to be alive a biological system must utilize some resources, like food, for example. Where can a system get food? Only from outside itself (it cannot eat itself and keep a long life). In the peoples world it means usually – from other people, but instead of taking an actual food or something we take money as the universal equivalent of any goods. But we do not print any money by ourselves. The other people give them to us, but usually it is not a gift, usually they give money to us in the exchange for something they need from us. So, the logical chain is simple; to support our life we need resources, to get that resources we need money, to get money we need to give out to other people something they need from us.
Let’s say it shorter, to support our life we need to be needed!
We are successful until we are needed; we are successful until there are other people who want something from us. This idea governs our life from the birthday to the death. Everybody obeys to this “rule of life” unconsciously, just because we all are biological systems. It is good to be needed, but what if we feel a risk to become being not-needed? Our brain can always feel these things and when it does happen the brain starts looking for any way to escape that kind of a risk and keep us being needed – even if consciously we do not have any suspicions on what is going on. Can you imagine what people are going to do if they see/understand the risk to become not-needed (recall all the movies on CIA or so, where some bad guy from the agency wants to blow up civilians pretending the terrorists did it only because the government wants to cut off his budget)?
So, people always want to be needed. Sometimes to keep themselves to be needed people even fake (consciously or unconsciously) the necessity of the work they are doing. I mean, they do everything to convince other people (and themselves at the first place) that the work they are doing is really important and useful and promising and etc, etc, etc. But the truth is that work is needed to the authors of the work only.
Two kinds of professionals (beyond just salesmen) used to be very persuasive in convincing of importance of their work – politicians and researchers. The difference is that politicians usually do it on purpose (absolutely consciously), though researchers usually do it unconsciously.
But the fact is that today you can find lots of research, which are not needed to anybody but the authors, especially if you take a look on the field of educational research.
There is, of course, an important question, how can one estimate the valueless/ value-ness of research? There is not a general answer on this question, but I would offer my view on the educational researches.
Talking abut education and all stuff connected with it we should consider the whole system of education as “salesman – customer” relationships. The main rule for that kind of relationships is that; if customer does not want to by a product, hence salesman must invent something new to sell or go out the market.
Who is a central person, which must being considered as a most important costumer among such professionals as teachers, researchers, officials and politicians?
It might sound strange, but researchers, officials and politicians are not really interested in significant improvement of system of education. Why? Because if everybody had already a prefect school, prefect college and get a prefect education, all those “big fishes” would went out of job (hence, out of money). I do not want to say that every researcher, official or politician is faking the importance/necessity of him/her work. All I want to say that there is a tendency – hence, possibility – that some person can do that. Plus, the people who do not connect to kids directly have the tendency for not caring about the every day school life; they care more about keeping the job, pleasing the boss, getting the funds etc.
But there is a professional, who is really looking forward for the prefect educational system, at least for as-good-as-possible system of education. This professional is a teacher. It is obvious, that the better school, college, textbooks, curriculum, etc, etc, the easier the teacher’s job. Only a teacher is really interested in significant improvement of system of education (the teacher’s partner outside the educational system but also interested in that is a parent).
My logic leads us to a simple conclusion. In a system of education a teacher must play the role of a customer and researcher (official, politician) must play the role of a salesman. As a customer a teacher must make a decision on what textbook/curriculum/research/etc he/she wants to use to do the teaching work as good as it possible.
If we all agreed with this principle, we would have to reconsider the relationships between all the players on the field of education, but this is another story.