NL Video clip Equation Solving Fact Sheet
General information
Year of production:
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Mathematical Topic:
Technology:
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Related papers:
2009
the Netherlands
Dutch
18-19 year olds
A high achieving class of pre-university level students
Solving equations
Applet (Getal en Ruimte) embedded in Digital Mathematics Environment
(DME)
http://www.fi.uu.nl/dwo/gr-pilot/ for the applet and the tasks.
Students working individually with a netbook computer with internet access.
Male experienced teacher, but unexperienced in using technology in his
teaching
Drijvers, P. (in press). Teachers transforming resources into orchestrations. In
G. Gueudet, B. Pepin, & L. Trouche (Eds.), Mathematics Curriculum Material
and Teacher Development: from text to lived resources? (pp. - ). New
York/Berlin: Springer.
Starting situation
The video registration took place in the context of a pilot initiated by the publisher of the main Dutch
textbook series for secondary mathematics education. The publisher, seeking for ways to improve
their product and to integrate technology, decided to offer to their customers’ schools an online,
interactive version of a chapter on algebraic skills for grade 12, the final year of pre-university
secondary education. The skills addressed include solving equations and recognizing specific
equation types and corresponding solving strategies.
This teacher in this video initially volunteered for the pilot, but later intended to step back, because
on the one hand computer facilities in school were insufficient and on the other hand his students
objected to the idea of practicing algebraic skills with the computer, whereas they would need to
master them with paper and pencil in the national central examination. Concerning the first issue, we
were able to offer him a loan set of 30 netbook computers for the period of the teaching sequence.
On the students’ concerns, we convinced the teacher that practicing skills with computer tools was
expected to directly transfer into better by-hand skills. He spoke again with his students, and they
accepted to participate in the pilot. During the period of the pilot, this teacher had a heavy teaching
load, with 26 50-minutes lessons a week to teach, and an additional remedial teaching practice at
home. A technical assistant was available in school to set up the classes with the netbook computers,
and to make other practical arrangements such as charging the batteries, et cetera.
The grade 12 students were a few month before the national final examinations. They were eager to
practice their algebraic skills, as this seemed to be getting more important. The tasks in the online
module, therefore, are not new, but are mainly tasks to practice and refresh the students’ algebraic
skills. The teacher decided not to do any whole-class teaching, but to leave the students with the
online module and their personal netbook computers. He does use the white board for individual
explanations. In some occasions, he displays the overview of online student results through a data
projector (see below).
Task description
The task discussed in this clip is shown above. It concerns solving equations of the type A2=B2, where
A and B are algebraic expressions. Many students start to expand the squares and then get lost. See
for example the student work below.
It is only in the second line of the right screen, after many steps and a suggestion made by the
teacher, that the student notices an efficient solution strategy.
Clip description
The clip consists of two parts, taken from different lessons. In the first part, the teacher provides
individual help to a student who is working on the above task (even if the coefficients of the equation
may be different, due to task randomization). He uses the white board to explain the mathematical
issue.
In the second part, a similar individual explanation is provided, but this time the teacher uses the
netbook computer of another student to compare the results.
Transcript
Hey, you didn’t take the square root of it, that is 15.
No, I will write it down at the board, have a look.
I don’t have any chalk anymore, but look in this box here.
If it says a square is 225 x square, that a of course is 15x or minus 15x.
Because, if I square this, Evan, yes, I get 225 x squared. You get 225 squared.
_____________________________
But you have to use the rule A squared equals B squared means A equals B or A equals?
Minus B.
Correct.
Now you put the square root over it.
Do I have to say ‘or’?
I would not use the square root…
… easier …
…because after that there should be…
you took the square root of that…
Yeah, but for her [her neighbor] it says it is correct.
Do you still have it there? Put it beside.
The square root as well!
Yes, but in your case it is written so strangely.
No, I have exactly the same.