[I have now tried three times to post my comment, and each time Google fails to post it and loses my work. Forgive my brevity here; I have lost motivation to recreate this yet again. I have finally learned that I have to identify myself as anonymous for it to post. Don't be fooled - I am me, Dean.]
I found the idea of UNIT FRACTION to be important and interesting. What was most interesting was how unit fractions can help students understand fractions like counting by 1s helped students understand whole numbers. "Just as every whole number is obtained by combining a sufficient number of 1s, every fraction is obtained by combining a sufficient number of unit fractions." The idea of unit fractions are used again and again, when comparing fractions, to adding and subtracting fractions, to multiplication of fractions.
Although I won't be introducing the idea of fractions to students in middles school, I would still emphasize the two important aspects of fractions: the whole and the equal parts. The magnitude of a unit fraction will depend on how many equal parts the whole was divided into. When working with visuals and manipulatives, I would encourage students to identify the unit fraction, to reinforce the concept.
Dean you might be surprised about introducing the basic ideas of fractions to middle school students. I have been finding to many students truly not understanding the fraction concept of one and what it means for the fractions to have parts of equal size. The idea of adding fractions is always parts and there relation to making a whole is new to some students. Use formative assessment next year for classroom entrance assessment to see what students know with each section of teaching with fractions.
I like how unit fractions can be used to clarify and compare the size of fractions. I find this really helpful. By looking at the denominators and numerators one can easily compare fractions: "The one with the larger denominator is smaller (p. 4)... for fractions that have the same numerator, the fraction with the smaller denominator is greater (p. 4)."
Having just finished a fraction unit with 6th grade students I was so surprised the level at which we needed to start the teaching. It was so smart of my co-teacher and myself to do pre-assessment with the unit. Knowledge that the students should have had with adding and subtracting with unlike denominators, what was one and how to use this as an estimation tool, how to double or half fractions and so much more was missing. So teaching division of fractions was on hold with all except about eight students out of 70! I found the idea of number lines and models had not been used or fully understood so that it almost seemed like new teaching with the students. The inability to put the numbers on a number line demonstrated the most important idea to me that the students did not have a value associated with a fraction (some students were looking at fractions as two numbers and not one number that could be placed on a number line!) So the develop of skills by grades was not important to me. Understanding the use of formative assessment and the sequence of development (maybe this is why we should look at grade development) was important in my teaching the unit. Ironically, we have moved on to percentages and found that the base ten idea of 10% tip...move the decimal point or add 5 ten's for fifty percent should have been a slam dunk, but many students did not generalize the information because the language we used was slightly different! The use of formative assessment has proven to be the most important tool for our planning.
[I have now tried three times to post my comment, and each time Google fails to post it and loses my work. Forgive my brevity here; I have lost motivation to recreate this yet again. I have finally learned that I have to identify myself as anonymous for it to post. Don't be fooled - I am me, Dean.]
ReplyDeleteI found the idea of UNIT FRACTION to be important and interesting. What was most interesting was how unit fractions can help students understand fractions like counting by 1s helped students understand whole numbers. "Just as every whole number is obtained by combining a sufficient number of 1s, every fraction is obtained by combining a sufficient number of unit fractions." The idea of unit fractions are used again and again, when comparing fractions, to adding and subtracting fractions, to multiplication of fractions.
Although I won't be introducing the idea of fractions to students in middles school, I would still emphasize the two important aspects of fractions: the whole and the equal parts. The magnitude of a unit fraction will depend on how many equal parts the whole was divided into. When working with visuals and manipulatives, I would encourage students to identify the unit fraction, to reinforce the concept.
Dean you might be surprised about introducing the basic ideas of fractions to middle school students. I have been finding to many students truly not understanding the fraction concept of one and what it means for the fractions to have parts of equal size. The idea of adding fractions is always parts and there relation to making a whole is new to some students. Use formative assessment next year for classroom entrance assessment to see what students know with each section of teaching with fractions.
DeleteI like how unit fractions can be used to clarify and compare the size of fractions. I find this really helpful. By looking at the denominators and numerators one can easily compare fractions: "The one with the larger denominator is smaller (p. 4)... for fractions that have the same numerator, the fraction with the smaller denominator is greater (p. 4)."
ReplyDeleteHaving just finished a fraction unit with 6th grade students I was so surprised the level at which we needed to start the teaching. It was so smart of my co-teacher and myself to do pre-assessment with the unit. Knowledge that the students should have had with adding and subtracting with unlike denominators, what was one and how to use this as an estimation tool, how to double or half fractions and so much more was missing. So teaching division of fractions was on hold with all except about eight students out of 70! I found the idea of number lines and models had not been used or fully understood so that it almost seemed like new teaching with the students. The inability to put the numbers on a number line demonstrated the most important idea to me that the students did not have a value associated with a fraction (some students were looking at fractions as two numbers and not one number that could be placed on a number line!) So the develop of skills by grades was not important to me. Understanding the use of formative assessment and the sequence of development (maybe this is why we should look at grade development) was important in my teaching the unit. Ironically, we have moved on to percentages and found that the base ten idea of 10% tip...move the decimal point or add 5 ten's for fifty percent should have been a slam dunk, but many students did not generalize the information because the language we used was slightly different! The use of formative assessment has proven to be the most important tool for our planning.
ReplyDelete