Failure... then success
There seems to be a widely held assumption that I am patient. I am not patient, not in the very least, and I'm sure my children would be the first to stand in line to tell you so. Just because you homeschool does not suddenly imbue you with patience, nor does having a large family. Someone commented to me just yesterday that I must be saint because I have a lot of children. Heh. No. Not even close. So sorry to disappoint. If anything homeschooling a large number of children assures that I will never be tempted to think I am particularly patient, and I certainly won't see myself as nearing sainthood. There are just too many instances in a day that remind me otherwise.
Take yesterday for example. Things were going well. Everyone had completed their math. We had all navigated our way through the idea of irregular plural nouns. (After having to go back and figure out exactly what 'plural' meant. It's a slow process.) And I was making my way around the table correcting each child's work in prelude to adding our Kenya maps to our travel journals. I get a certain child's workbook, and realize this child seemed to have not quite understood the math. So I ask this child to read the three digit numbers, 104 and 114, out loud.
From that moment on, this child and I pretty much went to Hell in a hand basket. The child couldn't read the numbers, though this wasn't actually all that new. When stressed, this child tends to stop thinking, and starts to blurt out whatever non-nonsensical thing that happens across the misfiring brain. I will admit that unthinking, non-nonsensical answers are a little bit of a trigger for me. I don't mind genuine mistakes, but the verbal spewage of nonsense acts the same way on me as a red flag waved in front of a bull. Things continued to deteriorate, and when I discovered that I was scrawling the words 'hundred' and 'thousand' across the entire workbook page, I was still coherent enough to call a time out.
The child went and banged play-doh around with the others who were waiting for my attention, while I stomped into the kitchen, reheated a cup of coffee, and texted a long, ranting, frustrated text to J. (Lucky man.) We, the child and I, both took a few minutes to regroup and catch our collective breath.
After a few more deep breaths, I could feel my own thinking brain come back on line a bit, and I pondered the less than stellar past fifteen minutes. If I am honest, my irritation didn't stem from the child not getting the answer right. At the root of my irritation, as so often happens, was just plain fear. Fear that we had finally reached the plateau that I dread. Fear that perhaps this child has gone backwards. Fear that I'm not doing enough. Lots and lots of fear. Once I could breath and take a break, I realized that this was all pretty misplaced. The rational part of my brain was telling me, it could very well be as simple as not enough time having worked with place value.
Teaching place value. That, I can do. I've taught ten other children to understand place value. I have a lot of tricks. I've got this. The earth continues to spin, and the tension in the room continued to settle.
Breath.
I let the child continue to pound dough while I got out my supplies. So much of math depends upon understanding place value. I've found with my people that until they have physically worked with the idea of place value, they just don't get it. Here's what I have found to be most helpful.
Those are dry erase boards, and I'm using one for each place. Before it was erased, I also wrote at the bottom which place value it was. Up above are manipulatives in ones, tens, hundreds, and there is even a thousand block. We start out with just the ones (or units or loose squares, whatever will make sense to the child), laying out a number of them and then writing that number on the board. Then we see how nine loose squares like to join themselves into long stacks when a tenth is added, and we add the tens board. We do the same thing... laying out a number with the manipulatives and then writing what we have laid out. I'll then switch it, asking for the written number first, then the picture of it above. Or I'll have the child lay out the picture of a number I say. Once this seems to be understood, we add the hundreds board, looking at how the set of ten, ten rods like to stick together in a square. The process then continues. It is at this point that we can also talk about how important zero is to hold a place, showing what the number would be without a zero by taking that board away. It is so much easier to see what is going on when you can move the objects represented by the numbers around.
This is just step one, and by the end, the child in question could read and lay out every number I suggested. It will probably take a couple of weeks of doing this to really cement it, but after my apology and some work together, we were both well ahead of where we started.
The next step after basic place value is the idea of carrying and then borrowing, which are also much more easily taught in this fashion than just with a paper and pencil. Of course, you really need to be able to regroup that stack of tens into single squares, so I switch out the manipulative and use unifix cubes instead.
I also use the dry erase boards representing place value and we physically group and regroup the cubes followed by writing on the boards what we've done. I will do this for weeks if necessary before ever asking a child to borrow and carry with just a problem on a piece of paper. I will also always allow a child to use these to do math problems for as along as they need/desire to.
Why rush? This is such basic groundwork that it needs to be extremely firm and understood in a variety of ways. A firm base on which to build allow for faster learning later. This was my mistake way at the beginning of the day. I assumed we had reached a place we had not, and instead of immediately going back to check the basic understanding, I lost my cool that it wasn't there.
No, not patient.
________
Liturgy post... The Beginnings of a Solution
Take yesterday for example. Things were going well. Everyone had completed their math. We had all navigated our way through the idea of irregular plural nouns. (After having to go back and figure out exactly what 'plural' meant. It's a slow process.) And I was making my way around the table correcting each child's work in prelude to adding our Kenya maps to our travel journals. I get a certain child's workbook, and realize this child seemed to have not quite understood the math. So I ask this child to read the three digit numbers, 104 and 114, out loud.
From that moment on, this child and I pretty much went to Hell in a hand basket. The child couldn't read the numbers, though this wasn't actually all that new. When stressed, this child tends to stop thinking, and starts to blurt out whatever non-nonsensical thing that happens across the misfiring brain. I will admit that unthinking, non-nonsensical answers are a little bit of a trigger for me. I don't mind genuine mistakes, but the verbal spewage of nonsense acts the same way on me as a red flag waved in front of a bull. Things continued to deteriorate, and when I discovered that I was scrawling the words 'hundred' and 'thousand' across the entire workbook page, I was still coherent enough to call a time out.
The child went and banged play-doh around with the others who were waiting for my attention, while I stomped into the kitchen, reheated a cup of coffee, and texted a long, ranting, frustrated text to J. (Lucky man.) We, the child and I, both took a few minutes to regroup and catch our collective breath.
After a few more deep breaths, I could feel my own thinking brain come back on line a bit, and I pondered the less than stellar past fifteen minutes. If I am honest, my irritation didn't stem from the child not getting the answer right. At the root of my irritation, as so often happens, was just plain fear. Fear that we had finally reached the plateau that I dread. Fear that perhaps this child has gone backwards. Fear that I'm not doing enough. Lots and lots of fear. Once I could breath and take a break, I realized that this was all pretty misplaced. The rational part of my brain was telling me, it could very well be as simple as not enough time having worked with place value.
Teaching place value. That, I can do. I've taught ten other children to understand place value. I have a lot of tricks. I've got this. The earth continues to spin, and the tension in the room continued to settle.
Breath.
I let the child continue to pound dough while I got out my supplies. So much of math depends upon understanding place value. I've found with my people that until they have physically worked with the idea of place value, they just don't get it. Here's what I have found to be most helpful.
Those are dry erase boards, and I'm using one for each place. Before it was erased, I also wrote at the bottom which place value it was. Up above are manipulatives in ones, tens, hundreds, and there is even a thousand block. We start out with just the ones (or units or loose squares, whatever will make sense to the child), laying out a number of them and then writing that number on the board. Then we see how nine loose squares like to join themselves into long stacks when a tenth is added, and we add the tens board. We do the same thing... laying out a number with the manipulatives and then writing what we have laid out. I'll then switch it, asking for the written number first, then the picture of it above. Or I'll have the child lay out the picture of a number I say. Once this seems to be understood, we add the hundreds board, looking at how the set of ten, ten rods like to stick together in a square. The process then continues. It is at this point that we can also talk about how important zero is to hold a place, showing what the number would be without a zero by taking that board away. It is so much easier to see what is going on when you can move the objects represented by the numbers around.
This is just step one, and by the end, the child in question could read and lay out every number I suggested. It will probably take a couple of weeks of doing this to really cement it, but after my apology and some work together, we were both well ahead of where we started.
The next step after basic place value is the idea of carrying and then borrowing, which are also much more easily taught in this fashion than just with a paper and pencil. Of course, you really need to be able to regroup that stack of tens into single squares, so I switch out the manipulative and use unifix cubes instead.
I also use the dry erase boards representing place value and we physically group and regroup the cubes followed by writing on the boards what we've done. I will do this for weeks if necessary before ever asking a child to borrow and carry with just a problem on a piece of paper. I will also always allow a child to use these to do math problems for as along as they need/desire to.
Why rush? This is such basic groundwork that it needs to be extremely firm and understood in a variety of ways. A firm base on which to build allow for faster learning later. This was my mistake way at the beginning of the day. I assumed we had reached a place we had not, and instead of immediately going back to check the basic understanding, I lost my cool that it wasn't there.
No, not patient.
________
Liturgy post... The Beginnings of a Solution
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