Math Place Value
It has never occurred to me how much the place value system has made our lives easier. Imagine having to count in nines or 15s. How would our money be counted? And what would happen of ratios and percentages. The consequences is mind-boggling.
Why am I thinking about place value? While it is something that might come naturally to most of us; there are some of us out there who don't really get it. This messes up pretty much number operations, decimals, ratios and percentages and other mathematical topics related to them.
Sofiyya, 9, is struggling with operations and is just coming to grabs with the concept of carrying over and borrowing. On my part, I cannot really empathise because I can't see why anyone cannot understand these processes. This led me to think about how something is 'learned' and understood. What happens when we try to solve a new problem or stage in the development of a particular knowledge? When do we understand? Is my inability to understand this situation preventing me from providing her with other means to learn?
While Ihsan has received the almost complete Montessori Math primary curriculum, Sofiyya has not had that opportunity as I juggled my various responsibilities. While she understood plots and dramas in storybooks meant for teenagers, she does not get the technicality of place value. I found that going back to hands-on materials helped but each time she had to do it in writing; she is unsure and does not get the tactics used despite repeated teaching.
Needless to say, I was exasperated. This was made worse when she had to put language and numbers together in word problems. She did not have the concept of what addition or subtraction stood for; something you have to infer from word problems. I had to teach her key words but this was not what I feel would be a long term solution. She could not conceptualise place value and operations. I cannot fathom why she couldn't.
I wonder if it was due to me using textbooks and workbooks instead of manipulatives with her early in primary school unlike with her brothers, because it was 'easier'. The ease of just using whatever were in those books have given me the illusion that she could be taught by just verbal explanation and symbols; I have skipped concrete and pictorial stimulation for straight, abstract symbols.
I feel that now I have to turn back and provide her with those concrete examples but am not able to do so in isolation and wait for her to be ready for the next stages considering she's already in primary 3. There is a need to show the authorities that she was on par with her level and so I have planned to do all three stages; to show subtraction with carrying in writing for example, I plan to use the manipulatives to teach her and for her to use them to answer the questions. She of course, would need to be taught how to do this without the manipulatives when she is firmer in her understanding.
The other matter that I am considering is whether I am teaching her the wrong way. I have used the methods and tactics that I myself was taught in school. What if my way was not how I should be teaching students like her? What if these methods are not the only ones (I have a strange feeling they aren't).
I have more questions than answers.
Why am I thinking about place value? While it is something that might come naturally to most of us; there are some of us out there who don't really get it. This messes up pretty much number operations, decimals, ratios and percentages and other mathematical topics related to them.
Sofiyya, 9, is struggling with operations and is just coming to grabs with the concept of carrying over and borrowing. On my part, I cannot really empathise because I can't see why anyone cannot understand these processes. This led me to think about how something is 'learned' and understood. What happens when we try to solve a new problem or stage in the development of a particular knowledge? When do we understand? Is my inability to understand this situation preventing me from providing her with other means to learn?
While Ihsan has received the almost complete Montessori Math primary curriculum, Sofiyya has not had that opportunity as I juggled my various responsibilities. While she understood plots and dramas in storybooks meant for teenagers, she does not get the technicality of place value. I found that going back to hands-on materials helped but each time she had to do it in writing; she is unsure and does not get the tactics used despite repeated teaching.
Needless to say, I was exasperated. This was made worse when she had to put language and numbers together in word problems. She did not have the concept of what addition or subtraction stood for; something you have to infer from word problems. I had to teach her key words but this was not what I feel would be a long term solution. She could not conceptualise place value and operations. I cannot fathom why she couldn't.
I wonder if it was due to me using textbooks and workbooks instead of manipulatives with her early in primary school unlike with her brothers, because it was 'easier'. The ease of just using whatever were in those books have given me the illusion that she could be taught by just verbal explanation and symbols; I have skipped concrete and pictorial stimulation for straight, abstract symbols.
I feel that now I have to turn back and provide her with those concrete examples but am not able to do so in isolation and wait for her to be ready for the next stages considering she's already in primary 3. There is a need to show the authorities that she was on par with her level and so I have planned to do all three stages; to show subtraction with carrying in writing for example, I plan to use the manipulatives to teach her and for her to use them to answer the questions. She of course, would need to be taught how to do this without the manipulatives when she is firmer in her understanding.
The other matter that I am considering is whether I am teaching her the wrong way. I have used the methods and tactics that I myself was taught in school. What if my way was not how I should be teaching students like her? What if these methods are not the only ones (I have a strange feeling they aren't).
I have more questions than answers.
Comments
Yes, Sofiyya's finally getting it now, although I do fear she'll forget now that we've moved on to multiplication. Sofi's in grade 3 too. Umayr's a grade behind in Math too (and he's sitting for PSLE next year!)However, we are more relaxed now that we have decided to HS everyone through secondary level. Happy homeschooling!