Section 1: Discussion of Content
Unlike other points of academic learning, the journal entitled Can there be research in mathematical education written by Herbert Wilf, points out that when it comes to developing the understanding about math, research procedures used in other academic lessons related to human sciences do not apply properly to mathematical subjects. Through taking the task of utilizing different mathematical research references, WIlf tried to seek different sections in the said researches that would prove the extensive relation of particular research procedures into improving teaching mathematics subjects through increasing their rate of efficacy. After carefully examining the references gathered y the author, he claims that since math is based on logic, process and formula, teachers are expected to create procedures that would improve the way they present each lesson to each student. Given that each student has a different process of learning, it could not be expected that one process of teaching will also work for the others at the same pace. Hence, the use of human samples to specifically be called as ‘general representations’ of the general public in particular researches in Math is not applicable in defining efficacy in teaching the said subjected. Wilf then further suggests that the utilization of general samples in mathematical research be abandoned as they do not work well for the said cause of improving teaching efficacy in the subject.
Section 2: Summary of Journal
The work of Stanley Ocken on algorithms, algebra and access is a journal study that identifies the primary flaws of teaching mathematics based on classical ways of understanding the logic behind the said subject. Relatively, he notes that when it comes to algorithms and long divisions, students have a hard time following the process. If there are those who can follow, most of these students are exceptionally able to concentrate on the process. This is the reason why there are instances when Math is said to be ‘not for everybody’. This affects the field of math drastically as it becomes the least appreciated subject among all the others in a university or any kind of learning institution at that.
Given that the world thrives under new circumstances of revolutionary teaching already, it could be recognized how the traditional way of teaching algorithms and algebra and all the other points of learning related to it could actually serve a ‘drag’ to teachers at present. It then suggests that instead of allowing the students to find their own ways of solving mathematical problems, improving the K-8 system in developing the young students’ mathematical skills plays a critical role in assisting students in the higher years of learning to get used to mathematical equations later on.
In relation to the applicability of this study based on the validity of the presentation of samples that the researcher used to present the data he points out to be vital in explaining the situation, it could be considered that the failure of presenting a single distinctive path of learning that students ought to follow makes the process rather weak. Although it suggests that improving K-8 mathematics based teachings could ease out the situation on teaching algorithm to higher years, it does not provide a single usable process to adapt to since there are anomalies when it come to defining such procedures according to the learning adaptation approach accepted by each student.
PART 2: Classroom Implementation
Section 1: Mathematics Teaching in Middle School
Considerably noted to be published by the National Council of Teachers of Mathematics of NCTM, this journal provides the recent news about the most efficient ways of teaching students regarding the different subjects included in learning math. When it comes to middle school students, it is essential that interaction be considered a crucial stage of learning. This is the reason why teachers are invited to become more creative in the way they present the subjects to their students in class. One of which is suggested in the journal. Using origami balloon cues to teach subjects of Linear Ratio, Volume Measurement and Area Measurement, the researchers found that the students’ interest on the subject increased and their application rate on the highlights of the said areas of learning improved as well. Allowing the students to know directly the dimensions of the origami they created improved their interest on knowing how to get or measure their work through using relative solutions under the lessons being presented to them in class. Stimulating their interest first through arts gives them a chance to explore the situation further and be hooked on the idea of gaining understanding on learning measuring procedures better.
Section 2: Curriculum Comparison
In the aim of improving the teaching of Mathematics to students at higher levels of learning, the improvement of the lower-grade teaching systems have been pursued to be applied by teachers. Relatively, the students are expected to follow a system of algorithmic way of learning allowing them to get used to the logic behind counting and calculating numbers at an early age. It is believed that through such improvements, children would adapt better to the different conditions of learning math as they mature further and take on more tedious tasks in accepting advanced math subjects later on. Strand-based learning is suggested to be used. This learning process invokes the need of the students to follow a continuous process of practice from kinder towards grade 8 as they master the different skills in math. Through this continuous pattern, students are expected to become more at ease as they work their way up to more complicated math problems. A particular comparison from the Manitoba teaching process with the example given on section 1 is that of the grade 2 teaching under the code 2.55.6 whereas the sorting of 2-D shapes and 3-D shapes is involved. This would allow students understanding sorting rule while also given the chance to learn more about volume, space and measurements.
National Council of Teachers of Mathematics (NCTM). (2003). Mathematics Teaching in Middle School.
Ocken, S. (2001). Algorithms, Algebra, and Access. The City College of the City University of New York. http://www.nychold.com/ocken-aaa01.pdf. (Retrieved on November 20, 2013).
Manitoba Education. Kindergarten to Grade 8 Mathematics: Manitoba Curriculum Framework of Outcomes 2013. http://www.edu.gov.mb.ca/k12/cur/math/framework_k-8/index.html. (Retrieved on November 20, 2013).
Wilf, H. Can there be “research in mathematical education”? http://www.math.upenn.edu/~wilf/website/PSUTalk.pdf. Retrieved on November 20, 2013).