5th Blogpost

Here we are nearly at the end of March, and we have been covering a large quantity of topics in MTH 329-01.  There is one  concept that I have come across while in MTH 329-01 that I feel the need to discuss, the idea of group work and collaboration in regards to the “teacher-student relationship and classroom environment”.

The basis for this comes from, primarily, two sources, my own experiences and the following:


In short, the “thesis” that the presenter puts forth equates student seating choice in the classroom with how well they perform or how attentive and engaged the student is in regards to the mathematical content being taught by the source of that knowledge i.e. the teacher.  The presenter then goes on to discuss how she combated the mindset of some students that “sitting in the back allows I [the student] to be non-involved with the learning process” by showing how she incorporated various technologies {clickers}, working in groups, and a more active/diverse approach to involving students’ in mathematics education by utilizing more “interesting and applicable” activities.   Personally, I think she has the right approach to getting student’s more active in their mathematics education, but I disagree with the mantra that group work and collaborative effort be the “end-all-cure-all” to help students.  I say this because I dislike group work of all forms; whether forced or unforced, due to the simple fact that in the “big” things in academics {tests} and in life [interviews, actual job, etc.] a person is on their own; hence, it seems counterproductive to encourage a “group mentality” mindset in students currently when they are, in essence, on their own when it comes to some of life’s “biggest” challenges.

Let me be clear though, I am NOT advocating for a child isolationist practice and a classroom environment where no one talks to each other, ever, and the teacher does nothing to engage his or her students, instead, I would prefer to see, at best, a more pro-option approach to student activities in class.  What this means is that teachers must, on day 1, set the tone that their classroom is a safe and nurturing place where it is okay to ask questions, but the responsibility to ask those questions is on the individual students themselves, NOT the group as a whole NOR the instructor.

Furthermore, all in class activities should be done in collaboration with classmates or solo, by choice of each student, but the teacher is equally ready to assist all students with any potential difficulties that arise as they proceed through the activity.

In adopting this approach, I believe teachers can still do their job, students can still show up and learn, but the responsibility for the actual learning rests with the student, not with the teacher.  Clearly, an issue then arises when trying to evaluate how “good” a teacher is, since, in the case of the students who ‘do not care’, will perform poorly on assessments; thus, when a teacher’s performance review is heavily based on assessment scores, that teacher, even if they do a “good” job with every student, and everyone of those students makes their own choice to engage or not, then the instructor is still held liable for the “poor” performance of those students who consciously made the choice to not engage both with their peers and their instructor in regards to the taught material.

The end result of adopting this viewpoint towards teacher-student relationships and the atmosphere in the classroom will be to produce students who are capable, independent individuals who can rationally react to a wide variety of mathematical (and other) contexts and proceed accordingly; while, simultaneously, grooming each adult to be better prepared for “real life” in USA.  I say this because, as a society/country, we strive for completion, independence, and honor the individual accomplishment; hence, the students who become so used to relying on a group to get through mathematical {or other} activities in school will be double burdened when confronted with assessments that they must complete completely by themselves and in a society that demands/expects each person to be rational and to be able to “stand on their own two feet”.

In summation, a powerful balance must be struck between the current trend in all education for “collaborative efforts” and the “traditional” individual work done in academics.  This balance can be found in the form of a compromise where each individual student has the choice to either have more group work available to them or each student can work independently while still having equal access  to teacher support regardless of being in a group or working solo.  The desired outcome of this compromise should be to create students who are more able to express their choices and be aware of the cost/loss of each choice they make while being more ready to deal with a reality that promotes the individual and independence over collaboration and reliance.

4th Blogpost

In the last few weeks, we have focused on the relationship between fractions, decimals, and operations on both of them.  Personally, I feel it is important to start by introducing fractions in a manner that students already have an intuitive understanding of i.e. “one-half”, “one-third”, “one-fourth”, etc. and then introducing the symbolic representation of those words: 1/2, 1/3, 1/4, and so on.  Once they grasp this, move towards introducing concept of equivalent fractions, perhaps using Bizz-buzz or some other format/context, and progress directly to basic operations on fractions.  Finally, we should wrap up this unit by “raising the level” and performing multiple operations on various fractions, both proper and improper, and seeing if students can relationally visualize/explain how/why their answer is correct.

Next, introducing the idea of decimals should follow a similar pattern as fractions, but I would personally skip multiplication and division of decimals because that is almost never done manually nor is it “real world applicable”, plus we just bust out a calculator if presented with decimals anyways, so why not stick with that trend.  Instead, I would like to focus on how decimals and fractions are related [1/2= .5=.50=.500 etc.] and emphasize that pronunciation of decimals “tenths” “hundredths” “thousandths” etc. will really help student’s comprehension of what decimals are and how to write them.  As for addition, subtraction, and ordering of decimals, Professor John Golden introduced a phenomenal game called “Decimal Point pickle” in which students must organize 3 drawn cards (from a standard deck) into decimals and then organize them in proper order.  For more details, see the following link:


Finally, we @ GVSU just finished our Spring Break, and I used that time to conduct my requisite 12 hours of observation @ the middle school level and to conduct some student task interviews.  This experience was a good one, and I got to experience more “behind the scenes” activities of what goes into being a K-12 teacher.  A specific thing that was brought to my attention via my discussions with my supporting teacher was that all the changes in educational standards and standardized tests really make their job simultaneously easier and harder.  Teaching becomes easier when you are given a set of objectives and the final test all pre-made to measure final knowledge in a unit/subject, but it becomes harder to both prepare for such a standardization, and then to develop lesson plans, activities, discussion points, etc. that align with the new curriculum such that they also assist with student learning and understanding of the material.  A common complaint I repeatedly heard was the lack of funds/resources and time for teachers to have to both meet these demands, and to provide ideal instruction to all classes of students.  The issue is, no one has any one clear cut solution that adequately solves all of these problems, so they will fester until significant changes (governmental, curriculum-al, sociological, etc.) regarding views/expectations of teachers and education.

Overall, we have brought up several important ideas regarding decimals and fractions and their presentation to students; however, a small sample of field work that I did reveals a growing divide between the ideal theoretical that is discussed in university education courses and reality of K-12 schools.  That being said, I did think of a solution to the time issue in regards to 2-hour delays, snow days, and length of school days/classes.

Currently, schools run from September-June, with a 3-month Summer vacation , so what I propose is to have a 3-month Winter vacation running from approximately Christmas time in December till end of March/beginning of April.  This completely removes approximately all issues of Snow Days and delays, thus reducing burdens on teachers to play “catch up” with material.  As for school length/class length, I think having somewhere around exactly 60 minutes per class with around 5-8 classes (depending on district, state, etc.) with lunch/recess of 30-60 minutes will help the overall flow of the day better for all involved.  Obviously a ton more detail and planning for logistical support would need to be done to implement this, but I believe that this set up could significantly reduce the time crunches that teachers always seem to feel.

Hope this is a useful/helpful/thought provoking post for all of who who have taken the time to read this.