Timed testing is the
part of Mathematics teaching and learning processes since time immemorial. The
teachers and university admission cells are in practice to take the timed
Mathematics test, since ages in Pakistan and around the globe. These tests are
commonly known as ‘mental-math tests’. In these tests, students are asked to
solve a mathematical problem within a minute. However, the complexity of these
mathematical problems varies as per the age, for e.g. Six years old are
expected to do the problems involving basic operations, whereas a high school
graduate is asked to do more complex question including surds, exponents,
algebraic equations, etc. Hence, timed-testing in math, continues from early-year
schooling to admission tests at colleges and universities. However, keeping in
view the complexity of questions the time is extended from 20 seconds in class
tests to 1 minute in college entrance tests. But the question to ask is, are
these timed-tests beneficial?
The perceived goal of
timed-testing is to develop mathematical fluency, so that the students are able
to solve mathematical problems fluently. Nonetheless, this fluency is often
associated with speed. Moreover, it is considered that ‘Good Mathematics is
speedy Mathematics’. However, the opposite is true, Mathematics is about depth
and not speed. Neuroscientists have suggested that Mathematics should never be
associated with speed, because many mathematicians are slow thinkers. One such
mathematician, Laurent Schwartz, a Fields medal winner, highlights that he
considered himself to be ‘unintelligent’ during school-time, because he was
slow in mathematical problem-solving. He further states in his autobiography
that “At the end of the eleventh grade, I took the measure of the situation,
and came to the conclusion that rapidity doesn't have a precise relation to
intelligence. What is important is to deeply understand things and their
relations to each other. This is where the intelligence lies. The fact of being
quick or slow isn't really relevant”. Hence, he disregarded the importance of
speed and re-shifted the focus from fast and furious solutions of math problems
to in-depth exploration of mathematical concepts.
Research also suggests
that when children encounter timed-tests, they feel anxious and stressful. This
stress occupies the working memory. The working memory is the controller and
regulator of information that the brain processes. When students are given less
than a minute to solve mathematical problem, their working memory shuns and
problem-solving aptitude and interest in subject diminishes. Researches also
highlight that working on math problems don’t make children anxious, but
problem-solving in timed situations make children feel vulnerable. The damage
to working memory and anxiety for timed-tests expounds that there are some
people who can handle math, while others can’t. This segregation deprives a
larger population to think that Mathematics isn’t for them. Hence, they don’t
take interest in mathematics and deprive themselves with a lot of professions
that involve mathematics.
Beside creating
anxiousness and segregating people into math-people and non-math people, these
messages also discourage the students from deep thinking in mathematics and
force them to memorize the facts and ‘tricks’ which could help them to ace
others. Hence, the roots of rote-learning of mathematical formulas, tricks
and procedures are laid down very early in the childhood and entrenched
up-till higher education. Because of enculturation of timed-testing,
students get the habit of using the learnt formula, rather than seek
patterns to create the formula. Consequently, students are unable to solve
complex problems when ready-made formula isn’t given.
To check whether the
same anxiety exists in Pakistani context, I asked 29 pre-service teachers to
elicit their experiences and feelings about timed math tests. Almost 75 percent
of pre-service teachers stated that they felt scared, nervous, anxious and
terrible while timed-math tests. However, some of them wrongly considered
timed-testing to be beneficial in the development of mathematical fluency.
Hence, teachers in our contexts have less awareness about recent
developments in Neurosciences and Mathematics Education. Because of this, they
pass wrong messages to the students about the nature of Mathematics and wrongly
judge students’ capability. Resultantly, they deprive learners from exploring
the beauty of Mathematics.
To eliminate this
ingrained belief about the association of speed and Mathematics, there is a
dire need for teachers and parents to study current literature. Mathematics
Educators including Boaler and Dweck urge stakeholders to develop ‘number
sense’ in students. Number sense implies the sense of flexibility of
decomposing and re-forming numbers and explore number relationships. ‘Number
talks’ is an important strategy to develop number-sense, by engaging
students in the articulation of their thinking process. Other strategies
include the explorations of a number-relationships using hundred charts,
customized games, number-line, base 10 block, area model and so
forth. These strategies would enable children to develop mathematical thinking
and love for the subject.
Conclusively, this
article pleads mathematic teachers, parents and university admission cells to
stop terrifying the students in the name of ‘timed tests’ and help them unleash
the true beauty of Mathematics. This wouldn’t be possible until and unless we
wash out our previous beliefs about the usefulness of timed-testing in
Mathematics, with new developments in the field of Mathematics education. Thus,
to help students in discovering true Mathematics and developing love for it,
teachers and parents must know that the timed - testing is a destructive practice,
so we should give adequate time during tests.
Very True Zeenar ... Teachers usually have the perception that Maths is all about Speed not about depth but if I see my experience, I used to think in this way because I was bound to see Maths as a subject of speed because teachers usually have a lot to do in a limited time. Therefore they want their students to be fluent an speedious in Maths. However the fact is the opposite side. And the reason for taking the timed test is also to check the speed of doing Maths (which actually demolishes the beauty of Maths. But unfortunately this is what our Educational System is ... The system wants one who are good at calculation and are fluent however, it should be not in this way ... So the change is required at the system level to make deep thinker :-)
ReplyDeleteNida Moosani you are right ! I think we teachers and teacher educators must initiate this change and try to institutionalize it , so as to save our children from the curse of Timed Testing :)
ReplyDeleteTotally agreed. The best part was that you proved it logically,that when time limit is applied it stops the production of ideas.And once something is proved logically no one can deny it.
ReplyDeleteI second you in this matter.
P.S: A very nice research.
Thankyou Zunair Ali ... I hope teachers, parents and admission cells would also consider these ideas and alter their strategies accordingly :)
DeleteA Good Article for Teachers. And A Good Thought.
ReplyDeleteThanks Arsalan :)
DeleteZeear first I congratulate you for writing very good article. this will be really helpful for maths teacher but here I want to say something about our examinations system that is based on paper pencil test and for that test specified time allocation, and teachers also perceive that the students should have the ability to solve the problems speedy, what about this !
ReplyDeleteYou are very right that examination system need an entire shift to help students to understand mathematics in depth. However, i feel that our examination system still provide some time to students, to solve a question and the checkers are not looking for the right answer only but they take into consideration the process of solving it. Whereas in 'Mental Math tests' which is very common in early schooling and college entrance exams, the teachers are only concerned with the answers , which provide very negative messages to the students, that mathematics is just a performance subject where there thinking process and methodology is not valued.
DeleteI think another study about how timings in examinations effect the students' learning in mathematics could be an interesting one to undertake :) and this study might lead us to the interesting findings that could improve our practices :)
Also, shift in assessment from paper-pencil tests to the more formative exams, is surely another important recommendation to the examination boards, so as to shift the focus from one-time testing to assessment for learning, happening throughout the year ... :)
Good Job W3llDone
ReplyDeleteThankyou Mustafa Habibi :)
DeleteCongrats Zeenar for generating such an informative and provoking article while raising this common issue in teaching mathematics. Mathematics is considered as mother of science it provides solutions for problems regarding other sciences. mathematical problems should not be time bounded because any particular method is not an ultimate method to resolve mathematical issues. time math test is really destructive because it creates hinders for innovative methods to resolve the same mathematical problem and students always try to adopt the traditional methods to complete the task within the given time
ReplyDeleteVery True Ghulam Raza :) I hope people would avoid timed-testing and move towards the constructive way that we advocate :)
DeleteI agree with your point because timed math testing is one of the main reasons why young learners find math difficult and jump into hating it in future,this even includes me.I have always hated math and physics(numerical part) due to this.Timed testing basically tests how smart a student is,at rote learning the conventional and classroom taught method to solve a mathematical problem.It discourages strategical approach and problem solving skills because students run after scoring the highest marks but no one opt for becoming a good learner.Even schools and colleges focuses more on producing high achievers so that they can beat other's rankings instead of promoting these necessary approaches.Moreover, if the student finds the teacher's traditional method difficult s/he is left with no choice to go for another method or come up with his own way of solving the problem as this is highly discouraged by teacher/s and on the record teacher doesn't consider that method as an alternative strategy.They have to rote-learn that formula in their minds to solve a particular problem and there is no other way left for them. Otherwise they may lose marks or s/he would be depreciated.Schools and colleges should rather consider this as a serious issue and should make efforts against it as only this way students will find or regain their interest in the subject.In addition to that, i liked the way you brought the facts and figures and indulged neurological aspect in it.
ReplyDeleteThanks Shazveen Saleem for highlighting the issue from a student's perspective. I think if we student, teachers and parents can come together and strive to eliminate this practice from its root :)
Deleteamazing piece of research, Zeenar. I love maths but I was never quick in Mathematics, and that gave a negative image to the people. Maths is all about thinking process and fun and it shouldn't be limited to time. I wish that Teachers and educators understand this point and that they should convey the same aspect to the students also. Keep it up dear :)
ReplyDeleteThanks :)
DeleteI think i am of the same category who does math slowly...
Thanks for endorsing the shared point of view !
It is amazing read. I wish if every educational Institute could think on the same lines. You have highlighted many real points to it. Congratulations on such an incredible piece of writing
ReplyDeleteThanks Nida :)
DeleteThank you zeenar for raising a valid issue that has been neglected by many mathematics educators and teachers. No doubt this practice is completely a drill. And I think such teaching and learning practices could only drain the time and mental capacities of students. In more, such practices might create agitation and uneasiness among students towards mathematics learning. Therefore, I suggest teachers and educators to discourage such practices in mathematics learning to make learning efficient and meaningful for the students of the contemporary world in which learning demands mainly on analysis, application and creation of knowledge.
ReplyDeleteXee send it to a newspaper,
DeleteDear Shueb,
DeleteThank you for liking the article and endorsing the point of view shared!
however, i am not sure, whether sending it to a newspaper would worth? because i don't know whether newspaper accepts the published blog-posts or not!
Very nicely written I wonder what your say about the pressure of standardized testing on teachers and the way sometimes they end up teaching despite themselves
ReplyDeleteYou're right standardized testing puts a lot of pressure on teachers... and i agree, that these pressures many a times sift our teaching methodologies and what is left is lecture method in which facts are shared and students are asked to memorize.
DeleteThanks for this, Zeenar. I am a victim of this system, and lived in dread of maths.
ReplyDeleteI think many of us have faced the same system. But what matters is how we save others from the threats and make learning more interesting :)
DeleteVery Nice! For more better understanding please attached research methodology and other related paper work.
ReplyDeleteKeep it up!
Thankyou Suleman Sikandar for liking it.
DeleteHowever, i would like to mention upfront that a rigorous research study was not done, rather i just asked students' views within a pre-service teacher education setting.
Secondly, i liked that you asked about research methodology, which made me think that a complete research study can be conducted on a whole-school system (considering it as a case) so as to explore school wide perceptions about timed testing. moreover the population for the study could include the students and teachers in the schools and parents of those students.
Publishing the results after conducting a school-wide study, would give us the holistic approach and could guide us further.
Thanks for raising this question and opening a wide area for research :)
And i think it is better if we don't call it a research, because it doesn't fulfills the research criterion and just phrase it as a classroom inquiry :)
DeleteGood work zeeenar. I agree with your argument to support deep learning in fact deep learning is long lasting
ReplyDeleteThanks Ali for endorsing this :)
DeleteInteresting article :) I never thought on these lines ..
ReplyDeleteThanks
DeleteI agree to your thoughts, I personally found those speedy math tests nerve-wracking. I think students should be well equipped with the techniques to solve instead of how quickly they should solve a particular problem. I think, if these suggestions are taken on board, the testing/examining system will represent student learning more cohesively.
ReplyDeleteThanks a lot Lavina for seconding !!
Delete