[Music] for for [Music] single [Music] foree for the main lesson is that children think very differently from what we assume and they are very clever at inventing new ways of thinking that I think I just respect children more by knowing how they really how creative they are and uh the main point I make here is that traditional math Educators think that children learn arithmetic by internalizing from the environment so the teacher says that's right that's wrong and students are supposed to internalize that knowledge and P's constructivism shows us that arithmetic is something that is constructed
from inside the child through his thinking for foreign spee fore fore foreign spee foreign foreign for foreign fore speee foree fore fore for [Music] I understand mathematics very differently from what traditional Educators understand and P showed with 60 years of research that children develop logical mathematical knowledge and concepts of number and for traditional uh mathematics Educators they don't know anything about logical mathematical knowledge so they think that mathematics is a cultural heritage that uh gener ations constructed and the purpose of education is to feed this culture to the Next Generation so they put try to
put a lot of mathematics in the child's head and P showed that no children have to do their own thinking and so if they want to do remember 2 plus two they have to come to their own conclusion about what 2 + two is foree okay speech foreign speech fore fore fore foreign foree fore here there is no thinking it's mechanical obedience and they count count count that's three and right just a rule it's just a rule in obedience and mechanical Behavior count count count count that's four and right count count count count count count
count count that's so these are used officially but okay they're not the best thing that makes children think fore fore fore spee [Music] [Music] fore fore spee spee forign [Music] for I use games because games make children think very hard whereas here um maybe this is a time uh to talk about traditional education for traditional education okay they use this kind of worksheet and they tell children what to do so they say okay the way to get the answer is to count 1 2 3 and write three here count count count count and put the
answer here count count count so um this is a mechanical approach that tells children how to get the answer and children don't have to think so uh here uh the motivation for doing this kind of work is to satisfy the teacher who says you have to write answers here and once the teacher sees all the answers she is satisfied cards with small numbers like this is a one two and here's a three and here's a four so it's the same numbers that you see here okay and the way we play this game is first first
we deal the cards among three people and the object of the game is to find two cards that make five so if it's my turn first I turn over the top card and that's not two cards that make five so I have to throw discard it in the middle of a table and the next child turns over the top card and this does not make five so he has to discard it and the next child turns over his card and oh yeah with this these two cards he can keep these two cards there are advantages
in games and the First Advantage is the child's motivation so if the child is playing a game then he or she is playing to satisfy himself he likes to play cards but if he does a worksheet like this com it's for the teacher the teacher needs to be satisfied so so the motivation is wrong the second reason is that of feedback the teachers's response usually teachers correct these worksheets after school and she returns the worksheet the next day children just cannot remember what they did yesterday and they just don't care what they did yesterday whereas
in a game like this if a child uh gets this and this and says that's five the other children are going to complain immediately that's not fine so immediate feedback is much more educational than the next day and then there are many other reasons but if the teacher always corrects the children's answers children learn that the correct answer can come only from the teacher whereas if they play games the correctness is decided by the children [Applause] themselves fore spee foreign fore [Applause] [Applause] speech [Music] [Music] ah [Music] [Applause] [Music] fore teachers have known for a
long time that children like games but usually usually they say to children when you finish your worksheet you have to do it first and if you have time left over then as a reward children are allowed to play games so uh that's like uh bribing children and um also it is the uh good student who work fast at this tedious uh work who get to play games and the slow children who are counting on fingers and and working slowly don't get as much time in the United States uh there is a big pressure to produce
higher test scores and many teachers who don't don't know very much think that uh tests come in this form and therefore it's best to drill children on how to do this to get quickly results yes yes superficial results [Music] for [Applause] foree [Music] [Applause] when there is a problem like this 87 + 24 the traditional teacher says you have to start with the ones and seven and four is 11 so put down the one and carry the one and then one and 8 and two make 11 so this is what they have to do that's
the rule that they are given but if children do their own thinking universally they start with the 80 + 20 is 100 so this is what they do 20 is 100 and then they they do 7 + four is 11 and then I add them together and the answer is 11 111 so this is why it is harmful to children to be taught this Rule and uh I have lots of data that show how children do stupid stupid things uh and uh as a result of being taught these [Music] rules about 12% of the second
graders can understand so it's a small minority of advanced children who understand the teacher's explanation of this rule but the great majority other children don't understand what the teacher is explaining and so if you let them do their own thinking they invariably start at the other end and go in the other direction so I say that these algorithms are are harmful for two reasons number one children have to give up their own thinking to obey the teacher because their own thinking goes from 80 to 7 this way and the teacher says you have to start
here and go the other way and the only way to obey the teacher is by giving up your own thinking now the minute you give up your own thinking you become stupid what's the best way to to start it well first you have to understand the theory before you do anything so that's why I'm here uh to tell teachers about how children really think and usually they are shocked to find out my God the children children think very differently from they think that children think like adults and all they have to do is tell them
what to do and children will get [Music] answers [Music]
