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.