In an earlier post I mentioned the gap in my math education. I have since read two books on Montessori math, am halfway through one on Waldorf math and halfway through one on the history of the equation of symmetry. Whenever I study something I want to share it with my children. So in addition to our regular studies we have been doing a lot of other math, and especially studying with Montessori materials. I have gained so much respect for teaching in this concrete way that allows the children to choose what they are going to study without compulsion. Herein is another similarity to TJed Leadership education.
Brennen was introduced to using the rods and number board for addition.
Logan, Brennen, Aubrey and Seth were introduced to the geometric shaped insets. This activity is not always considered math. It develops the fine motor skills and control over the pencil before the children start writing, but it can lead to so many other things, including math and art.
I introduced Brennen to the division board. He loved it and spent almost an entire morning on it one day. With this activity the children pour out a number of little balls of their choice, in this case it was 82. They count the balls and write the number down and then put a "house" around it. They then decide how many skittles are going to share the balls-in Brennen's case it was almost always 9. They write the number of skittles they have chosen in front of the house and place that many skittles on the top of the board. Then they give every one balls one at a time until they can not give them out evenly. Whatever is left they have as the remainder. Then the student writes these down and starts over or puts the material away. I introduced this activity to Aubrey also, she did about three problems and then put it away, but she needed a concrete reference point for division, and even that much helped. After several days of begging I introduced it to Logan (the children aren't allowed to touch a material until they have been introduced to it). He is so far from abstraction with it, but that is okay. He built several problems and we both saw the need for him to work more with the sandpaper numbers as he still is not really writing.
Kamron continues to work through his Saxon 6/7 book. He enjoys it and almost always understands from reading the lessons on his own. He declines most other invites to some of the other concrete lessons, because "he already knows that stuff." I did do a hands on lesson with him on squares and cubes, square roots and cube roots. We built them and took them apart with rods, so he could see how they were formed and what they meant. He thought that was pretty neat. We also learned about angles of parallelograms by building paper ones.
Logan built the number quantities. He talks about this activity a lot, but he has not pulled it out again. His understanding in this area is now pretty good. When we do the sandpaper numbers he can place them in order, tell which is bigger etc. He has also begun building numbers, such as 82, 43 etc. and naming ones I build with the sandpaper numbers.
This is Aubrey's work with equivalent fractions. It was more of an exploration of materials than a formal lesson. She struggles a bit with understanding the quality of numbers and how they are related. One night everyone stayed up until about ten thirty showing Daddy different things they had been learning and it turned into a discussion of our number system, as Kevin tried to explain the relationships of decimals in the base ten system. They built numbers with rods, counted and talked about place value. At times she was frustrated, but the next day she got on her online math program, Aleks, and said I want to study decimals. At least she wasn't scared off the topic.
We have done other work, especially with geometric shapes and the quality of triangles and how they can form every other shape, except a circle. All of these studies lately have been rather fun and deeply satisfying. I think we will keep it up.