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I have been promoting the use of an amazing way to teach ALL the numbers tables by using the hands and fingers.
What do you think the advantages are to using your fingers as an abacus/human calculator? IMO, it is a crutch, like a calculator, that can de-emphasize mental "number sense" skills. It is likely (at least in the older grades) much slower (less efficient) than simple memorization of math facts, and using your fingers as a calculation platform could have long-term negative effects on competency IMO.
It also removes the preliminary training (and benefits) of "mental math" where students can learn to perform increasingly complex calculations in their heads, without manipulative/pencils. Perhaps it is most beneficial to the lowest performing students. I am not a math teacher (just a parent) so maybe I am missing something here? If my child's teacher were advocating this "finger" approach, I would have a big issue with it as I would not want my child "trained" in this way.
Interesting points Ivory and Linda... My 8th grade son is now taking HS Honors Geometry. I am wondering how much of last year's Algebra I content he will forget, or if some of this content will be integrated into Geometry. He will be taking Honors Algebra II next year as a freshman. His current Geometry course is very heavy proofs, which he likes - Geometry and logic are his strengths - but I hope he doesn't lose Algebra skills. He'll likely take an Algebra refresher course over the summer.
While my son is on the "traditional" Honors/AP math path, my 7th grade DD is in a non-traditional program. This program takes a few of the very top kids in the gifted math classes across the district (total class around 10 I think) and they attend advanced math class at the High School that integrates Algebra, Geometry, much problem solving, game theory, statistics, deeper concepts, etc. They are doing some very advanced stuff... Some of these kids go on to attend the top STEM high schools (e.g. Illinois Math & Science Academy) and have very successful careers, so they seem to do very well with this "integrated" advanced approach.
What do you think the advantages are to using your fingers as an abacus/human calculator? IMO, it is a crutch, like a calculator, that can de-emphasize mental "number sense" skills. It is likely (at least in the older grades) much slower (less efficient) than simple memorization of math facts, and using your fingers as a calculation platform could have long-term negative effects on competency IMO.
It also removes the preliminary training (and benefits) of "mental math" where students can learn to perform increasingly complex calculations in their heads, without manipulative/pencils. Perhaps it is most beneficial to the lowest performing students. I am not a math teacher (just a parent) so maybe I am missing something here? If my child's teacher were advocating this "finger" approach, I would have a big issue with it as I would not want my child "trained" in this way.
I have used this technique with olders students who never were able to memorize the Tables, and even had become traumatized by the long history of teachers trying to remediate the problem.
What I observed was that, these students avoided the frustration and embarrassment of answering with a guess, and instead, double checked using this Finger Multply N method.
Then, we asked to do "homework" by asking themselves, what number times another might be, they gradually did memonize the Tables.
I am sure that the traditional pedahohie requires the presence of a Numbers Facts Table in front of the student as he/she learn and prasctices the Tables.
But this Finger method has the advantage of always being on the ready, novelty, and the knowledge that the tables are always right there, even during a test or otherwise.
I have also gound that the exercise is highly acceptable to the students whether they already are confident of their Tables or a little weak.
This "novelty" and high acceptance is invaluable in what so often is a sterile boring classroom.
Interesting points Ivory and Linda... My 8th grade son is now taking HS Honors Geometry. I am wondering how much of last year's Algebra I content he will forget, or if some of this content will be integrated into Geometry. He will be taking Honors Algebra II next year as a freshman. His current Geometry course is very heavy proofs, which he likes - Geometry and logic are his strengths - but I hope he doesn't lose Algebra skills. He'll likely take an Algebra refresher course over the summer.
While my son is on the "traditional" Honors/AP math path, my 7th grade DD is in a non-traditional program. This program takes a few of the very top kids in the gifted math classes across the district (total class around 10 I think) and they attend advanced math class at the High School that integrates Algebra, Geometry, much problem solving, game theory, statistics, deeper concepts, etc. They are doing some very advanced stuff... Some of these kids go on to attend the top STEM high schools (e.g. Illinois Math & Science Academy) and have very successful careers, so they seem to do very well with this "integrated" advanced approach.
That is always a problem,... remembering the course work after what is/has been, really, Cramming, though it is fit into a whole term but never re-visited again.
What I recommend is a repetitious and organized note-taking methodology which is structured so the student can re-visit the whole subject again at any time.
The repetitious pattern of organization of the content has mnemonic effect, augmented by the ordering of the Topics in a meaningful way.
Interesting points Ivory and Linda... My 8th grade son is now taking HS Honors Geometry. I am wondering how much of last year's Algebra I content he will forget, or if some of this content will be integrated into Geometry. He will be taking Honors Algebra II next year as a freshman. His current Geometry course is very heavy proofs, which he likes - Geometry and logic are his strengths - but I hope he doesn't lose Algebra skills. He'll likely take an Algebra refresher course over the summer.
While my son is on the "traditional" Honors/AP math path, my 7th grade DD is in a non-traditional program. This program takes a few of the very top kids in the gifted math classes across the district (total class around 10 I think) and they attend advanced math class at the High School that integrates Algebra, Geometry, much problem solving, game theory, statistics, deeper concepts, etc. They are doing some very advanced stuff... Some of these kids go on to attend the top STEM high schools (e.g. Illinois Math & Science Academy) and have very successful careers, so they seem to do very well with this "integrated" advanced approach.
A good geometry course definitely integrates algebra into the class. Algebra, btw, should have an element of proof especially in honors algebra I.
My kids took the honors sequence and never lost skills. Math isn't like English or History. You need to use skills from the earlier course in the next one.
I have heard good reviews about the Singapore Math Method, especially how it emphasizes depth and building a solid foundation.
Yes, our schools adopted this math curriculum several years ago. I have been impressed with the method and results, especially the problem solving methods (e.g. using bar graphs to solve word problems). Supposedly the texts are 1 grade above U.S. level. So Singapore Book 6 is for a 7th grader. I know our math gifted classes use Singapore books that are only 1 year ahead of grade level, whereas the other textbooks they use are 2-4 years above grade level.
A good geometry course definitely integrates algebra into the class. Algebra, btw, should have an element of proof especially in honors algebra I.
My kids took the honors sequence and never lost skills. Math isn't like English or History. You need to use skills from the earlier course in the next one.
No geometry Course should ignore descartes Bridge which is the most important beak through from the ancient Euclidean Geometry into Algebra, via his Analytical Geometry.
It is also a great opportunity to lecture to an audience of students who will see the historical insight that changed the math world when Descartes demonstrated how one can prove congrience of triangles by measuring each leg on a graph paper and comparing them to another triangle placed elsewhere on that same graph paper.
The idea that he ordered the universe with coordinates and thereby gave an address to everything that exists is profound.
That our Algebra can compare all these things to each other make geometry the picture which images Reality in our mind.
Yes, our schools adopted this math curriculum several years ago. I have been impressed with the method and results, especially the problem solving methods (e.g. using bar graphs to solve word problems). Supposedly the texts are 1 grade above U.S. level. So Singapore Book 6 is for a 7th grader. I know our math gifted classes use Singapore books that are only 1 year ahead of grade level, whereas the other textbooks they use are 2-4 years above grade level.
How do those Singapore books teach Fractions/Decimals/Percentages?
I discovered to my amazement that inner city schools actually teach this same subject throughout High School over and again, using the same approaches in books with different covers, and the same chapters rearranged in order that the course looks different to the students.
Obviously, no one but the accelerated classes actually master this, and they are so discouraged that they do not even notice the same material and even text books are used in each clas, 9th, 10th, 11th, and 12th grade.
How do those Singapore books teach Fractions/Decimals/Percentages?
I discovered to my amazement that inner city schools actually teach this same subject throughout High School over and again, using the same approaches in books with different covers, and the same chapters rearranged in order that the course looks different to the students.
Obviously, no one but the accelerated classes actually master this, and they are so discouraged that they do not even notice the same material and even text books are used in each clas, 9th, 10th, 11th, and 12th grade.
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