Tonight, the class looked into division of fractions in a visual way, and we also learned that fractions are used as:
- measurement numbers (in quantity and must have a unit, like cm, or $)
- proportion numbers (represent proportion and no unit is required)
Some of the tasks we did in class were:
Example 1, Out of 3/4 (3 fourths), how many 1/2's are there?
Method 1: by calculation
3/4 divided by 2/4
=(3divided by 2) divided by (4divided by4)
= 1 1/2 divided by 1
= 1 1/2
Method 2: by visual
3/4 divided by 1/2 = 3/4 divided by 2/4.
That is to say, how many 2/4 can you see inside 3/4?
The answer is 1 1/2
Example 2, In 2 fifths, how many tenths are there?
Method 1: by calculation
2 fifths divided by 1 tenth
= 4 tenths divided by 1 tenth
= 4 divided by 1
= 4
2/5 is the same as 4/10 so we drew 10 units and shaded 4 of them.
From the picture, it is very clear that the answer is 4.
I think the usage of pictures and models are excellent ways of helping children to understand the concept of division in fractions. Problems that seem to be complicated can become easier to comprehend.
In Bloom's Taxonomy, there are different cognitive levels (cognitive porcesses):
Level 1 - Knowledge Level (eg. know what is the value of 5/7 -1/2)
Level 2 - Comprehension Level (able to use situation after you comprehend it)
Level 3 - Application Level
"The major idea of the taxonomy is that what educators want students to know (encompassed in statments of educational objectives) can be arranged in a hierachy from less to more complex. The levels are understood to be successive, so that one level must be mastered before the next level can be reached" (Huitt, 2011).
Knowing this framework will enable teachers to assess students' cognitive level. We can also design higher order level questions to facilitate and challenge our students for more extensive and elaborate answers. Below are some questions that can be asked under the categories defined by Bloom (Source: Types of questions based on Bloom's Taxonomy. Retrieved 30 August, 2011 from http://www2.honolulu.edu/facdev/guidebk/teachtip/questype.htm) :
Knowledge level:
-remembering
-recognizing
-recalling identification
-recalling information
* who, what, when, where, how...?
* describe
Comprehension level:
-interpreting
-translating from 1 medium to another
-describing in one's own word
-organisation and selection of facts and ideas
* retell ...
Application level:
-subdividing something to show how it is put together
-finding the underlying structure of a communication identifying motives
-seperation of a whole into component parts
* what are the parts or features of...?
* classify ... according to ...
* outline/diagram ...
* how does ... compare / contrast with ...?
* what evidence can you list for ...?Area and Measurement
We were asked to draw as many squares as we could on a piece of dotted paper. We then made comparisons and found out how many times the smallest square was smaller than other squares. We also drew different shapes by joining 4 dots. The class squeezed out their brain juice to think of different solutions to find out the area of different shapes. Some of the methods we used were:
1) cut and paste to compare
2) using halves (eg. dividing the square into halves)
3) using subtraction way to minus away unwanted areas
4) counting dots inside the shapes
For peculiar shapes, I find it easiest to use the subtraction method to take away the unwanted parts.
It was fun to see how many ways we could come out with, and Dr Yeap gave us time to let us think and discuss. In this lesson, I learned not to be eager to show students what the answers should be. Adults tend to give out exernal signals (eg. frown, smile, thumbs-up, etc.) for right or wrong answers. Children who are dependent on these artificial signs will have difficulty in independent thinking and decision making. We need to let them have the internal ability. We should ask them questions even if they have the correct answers, and let them explain and justify themselves.
Thank you Dr Yeap, for being so patient with us. You have set a good example of how a math teacher should be.
Citation: Huitt, W. (2011). Bloom et al.'s taxonomy of the cognitive domain. Educational Psychology Interactive. Valdosta, GA : Valdosta State University. Retrieved 30 August, 2011 from http://www.edpsycinteractive.org/topics/cognition/bloom.html[pdf]
No comments:
Post a Comment