Introduction
The article has explored several differences among mathematicians and mathematical educators which have generated sever debates. The differences are not based solely on difference on points of view but on poor communication and language used by the two groups. Therefore, the article focuses on areas which the two groups agree. For example, the two groups generally accepted the idea that algorithms are poorly taught. In addition they also agreed that, continuous practice is necessary in enabling learners to develop computational fluency, calculators should be used with caution to avoid interference in understanding the basic mathematical procedures, due to usefulness of algorithms learners should understand how and why algorithms work, to understand algebra learners must be conversant with fractions, when possible mathematics should be taught in real world context , various methods should be used in teaching mathematics to enhance students understanding and finally mathematics teachers should have in-depth understanding of mathematical concepts so as to effectively facilitate learning.
The topic of the article is not befitting because the article discusses areas where mathematicians and mathematics educators agree on. However, the title is ‘reaching a common ground in K-12 mathematics education’ meaning the content should be mainly on the different views of the two groups and a discussion of solving the differences which will then lead to a common view. Therefore, a title like ‘shared views on K-12 mathematics education’ may suit this article. This is because the article does not show whether any group was opposed to the views by stating their initial perspective and the discussion leading to an agreement.
The article has stressed that, in work place people need to understand mathematical procedures so that they can function effectively. This holds water; however, some jobs may not need mathematical knowledge at all the article does not propose an alternative curriculum for this group of learner who may grow to do such jobs. In addition, it does not propose ways in which mathematical educators can use to indentify learners who may grow to compose this fraction of labor force.
The article stresses the fact that some mathematical concepts are so fundamental such that they need a lot of practice up to the point where learners can automatic recall. However, It fails to consider that some learners may be generally lazy or may find it boring to practice. Though, the article proposes that this point is achievable by use of variety of instructional method fails to give examples agreeable by both groups. In addition, it failed to propose ways which mathematical educators can use to motivate learners because motivation is necessary in teaching learning process.
The article has proposed that calculators enhance learning of mathematics in lower grades however; they caution that it may as well hinder acquisition of important mathematical procedures. Regardless of this dilemma, the authors fail to propose ways in which calculators can be in cooperated effectively in learning mathematics. They should have recognized that a calculator should only be a device of enhancing speed and accuracy of learner in solving mathematics problems. They could have been clearly stated that teachers should only encourage use of calculators in practicing the already learned mathematical concepts. The article has been clear that graphing calculators enhance students understanding of functions especially after learners have the basic knowledge on graphs.
The groups have argued that when learning logarithms especially base of ten, learners enhance their understanding of place value, a topic introduced at lower grades. This means that a student who failed to understand this concept gets a second chance. At this point the authors failed to recognize the fact that, as learners acquires new mathematical ideas it is likely that they may understand prior concepts which they never understood. It could therefore be logical for them to provide the psychological explanation on how some learners may behave in vertical knowledge transfer.
Despite both groups agreeing that algorithm is an important concept they failed to justify its importance and relevance to learners after school life. This kind of argument made Bush, 25 to conclude in his article that, ‘there is disconnect between the mathematics student learn in school and the mathematics student might need outside school’. It could be important for these two groups to agree that for any topic to be included in mathematics its relevance to learners’ life after school should justify its inclusion.
The discussion on teaching pedagogy advocated for use of direct instruction together with small groups is generally acceptable. This is because they have stated clearly that different topics need different approach. They even went head and gave examples of some topics for each method. However, it could have been advisable for them to go through all topics in all the grades and give recommendation on which pedagogy is suitable for each topic. Thereafter, they can state tstate that, a teacher is not restricted to use the recommended method. This is because different learners may prefer the teacher to use a given method which is not recommended. In giving out this recommendation they should put into consideration the time available for learning mathematics in each grade because course content should be covered within a stipulated time. In the discussion mathematical educators did not provide the reason why they always prefer teacher centered teaching method which does not give chance for learners to reason or think mathematically.
The article has recommended teaching of mathematics in the context of the real world. This is quite commendable because it enhances learners understanding. The author also acknowledged that not all topics can be taught in real world context because some topics are quite abstract this has also been acknowledged by Bush, 25 in the article of improving research on mathematics learning and teaching in rural context. Bush, 25 admitted that, ‘’ Despite several national reform movements in mathematics education, students rarely have access to mathematics that matters. That is, the mathematics that many students learn is connected to neither them nor their community. Mathematics teaching often fails to challenge students or to provide them with the necessary knowledge for important life skills’’. It could therefore be important for the mathematicians and mathematical educators to find a way in which mathematics syllabus can be modified to meet the needs of learners so that they can advocate for its teaching in context of real world.
Both groups admitted that a fraction of learners find it difficult to understand mathematics concepts. They however, did not provide a clear alternative which the mathematics educators should use to enhance learning of this group or provide a simpler curriculum for this disadvantaged group. In addition, the groups did not propose the best method of forming discussion groups. They seem to fail to realize that some mathematics educators may prefer to mix students i.e. the weak ones with the bright one so as to enhance learning, while others prefer to group weak students so that they can learn at their own slow pace (laura, Courtney and Olivia, 28).
Conclusion
The two groups i.e. mathematicians and mathematical educators have listed some common grounds in learning mathematics. They have however failed to state their previous positions before they discussed and agreed on the matters enlisted in the article. This has made the title somehow irrelevant to the content. A topic like shared views on K-12 mathematics is therefore seen to be more appropriate. This is because in the introduction the authors clears state that the differences in views between mathematicians and mathematical educators is mainly attributable to on poor communication and language used by the two groups.
The article is opens communication between the two groups, they discussed and acknowledged several mathematical issues however they fail to provide details to make their ideas clear. For example, first they agreed that continues practice in mathematics is essential because it makes learners to automatically recall basic facts however, they did not propose any method of encouraging the practice. Second, they agreed that calculators facilitate learning however they may hinder the understanding of basic mathematical procedures despite this; they failed to state on when learners should be instructed to use them to avoid the identified weakness. Third, they acknowledged that algorithms are poorly taught despite being an important mathematical topic however, they did not provide any way of improving teaching the topic. The lastly issue which did not come out clearly is that, though they agreed that it is up to the teacher to choose the best instructional method and just like in the other areas they failed to give guidelines on how mathematical teachers can choose the best instructional method.
References
Goe, Laura, countney Bell, and olivia little. "approaches to evaluating teacher effectiveness: A research synthesis." national comprehensive 1.5 (2008): 22. Print.
Ferber, Dan. "Raising their game." after a decade. N.p., 10 Nov. 2011. Web. 11 Aug. 2012.
