Haustið 2014 var gerð könnun á stærðfræðikunnáttu nýnema við Kennaradeild
Menntavísindasviðs Háskóla Íslands. Lagður var fyrir listi með spurningum úr
hefðbundinni grunnskólastærðfræði sem áður hafði verið lagður fyrir árið 1992. Í
greininni er sagt frá helstu niðurstöðum og árangur þátttakenda árið 2014 borinn
saman við árangur þeirra sem þreyttu sama könnunarpróf 22 árum áður. Niðurstöður
árið 1992 ollu vonbrigðum og áhyggjum rannsakenda, frammistaða þátttakenda
reyndist að flestu leyti lakari en búist var við. Árið 2014 reyndist árangurinn enn
lakari en áður því meðaltal hlutfalls réttra svara fór úr 53% niður í 44%. Ýmsar
nýlegar rannsóknir og skýrslur gefa einnig til kynna að stærðfræðilegan undirbúning
grunnskólakennara þurfi að auka og bæta. Í þorra tilfella er formlegt stærðfræðinám
grunnskólakennara lítið umfram það stærðfræðinám sem þeir búa að úr grunn- og
framhaldsskóla. Staða nýnema er því verðugt athugunarefni þar sem fæstir þeirra
bæta við sig miklu námi í stærðfræði í kennaranámi. Í greininni eru settar fram
hugleiðingar um viðbrögð við niðurstöðum könnunarinnar.
In 1992 a group of first year students at the University of Education (now the School
of Education of the University of Iceland), took a pre-assessment in mathematics. In
2014, 22 years later, the exact same questionnaire was given to a group of students
entering the Faculty of Teacher Education of the School of Education.
The test consists of 30 questions or problems from standard school mathematics,
involving numbers, calculations and algebra, e.g., the addition of fractions or the
solution of a linear equation, problems from geometry, e.g., the estimation of the
area of a square and a circle, a few problems from combinatorics, e.g., determining
the number of games in a round-robin chess tournament and some word problems
requiring relatively simple problem-solving skills. All the problems are multiplechoice with exactly one choice being correct.
A primary purpose of this examination was the evaluation of the mathematical skills
of the students in question, when starting their Teacher Education program. Secondly,
with two similar groups of students and questions being the same in both cases, a
comparison of results from 1992 and 2014 seemed a highly interesting objective.
Thirdly, a consideration of the results could offer indications for anyone involved in
the planning of teacher education.
Over the past decades, programs at the School of Education have frequently been
revised, perhaps the greatest single change being the step from a three-year teacher
education to the present five-year system. As for mathematics and mathematics
education in the programs, such courses have generally amounted to 3-4% of study
units so the mathematical background of most primary school teachers is more or less
their background from studies before entering the School of Education. Studies and
tests at the School of Education and the School of Engineering and Natural Sciences
suggest that the mathematical skill and success of university students depends on
previous studies, a determining factor being the number of mathematics courses or
mathematics credits taken. A recent study of the mathematical content knowledge of
prospective teachers highlights the need for mathematics for all prospective teachers,
not only those specializing in mathematics teaching.
This article presents some main results obtained from a pre-assessment in 2014. The
percentage of correct answers to each problem is given, and these figures can be
compared in a straightforward manner to similar scores from 1992. Results can also be
contemplated in view of the prediction made by the two authors of the questionnaire,
both mathematics teachers at the University of Education at the time.
Results from the 1992 test were generally considered to be disappointing. On most
problems, student performance was below prediction. Out of the total number of
answers given 53% were correct. Results from 2014 were poorer still, with 44%
correct answers. Success did not vary considerably between fields; students did
relatively better on problems from geometry and logic, and relatively worse on
problems involving numbers, calculations or algebra.
An average of 44% on the test in question must be considered low, and the considerable
drop from 53% in 1992 to 44% in 2014 is a cause for concern. It must be pointed
out, that two decades ago teacher education was a popular choice for students. With
an abundance of applications, student admission was subject to several conditions.
This popularity of teacher education is no longer the case and in recent years most
applications have been accepted. Variable conditions of admission may provide a
partial explanation for the drop in mathematical performance.
From the results of a simple investigation such as this one, only modest conclusions
can be drawn. In many cases, participants have not had much to do with school
mathematics for years. Their performance on the pre-assessment can definitely not be
considered to reflect the full extent of their mathematical competencies.
Several findings, including the results of the PISA studies, have indicated that
mathematics teaching in Icelandic schools could be more effective and fruitful, and
the results of this investigation add yet another uncomfortable fact. The crucial role
of teachers is widely acknowledged and all due efforts to reform must certainly put
the focus on teacher education.
