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Sequence 3What is the importance of these tendencies for human devel- opment? Each of these tendencies is instrumental in identifying… |
Sequence 4The tendency for work encourages doing/making, for 111m1ip11/atio11 allows one to fashion to one's purpose, for… |
Sequence 5the thinking of oth- ers. This thinking of others stimulates the human being to further think- ing and advances knowledge… |
Sequence 6conditions of its environment. The tendencies arc exactly what al- lows human beings to live under a variety of conditions.… |
Sequence 7live a satisfying life. It is this adaptive power that lies at the heart of development. One might say that development… |
Sequence 8being to the environment with respect to anything that is noticed and explored. This pattern seems to be applicable to the… |
Sequence 9• Learn the names associated with what you see. The names will help you remember the images you have formed through your… |
Sequence 10The adult has to work from the premises of the human tenden- cies. The capacities to explore, orient, communicate/name,… |
Sequence 11to experience quantitative situations in the environment. The child learns numbers to ten including counting, symbols, one-to-… |
Sequence 12j.., atlL•ntiH~ to the adult. Work h,,bih that dcpL•nd on allowing thl• tL•ndl'ncies to cnwrge whik• working in a natural… |
Sequence 1MONTESSORI MATHEMATICS: A N EUROSCIENTIFIC PERSPECTIVE by Benedetto Scoppola Benedetto Scoppoln joi11s t/1e Montessori world… |
Sequence 2cooperation with persons all over the world. Please let me know if you are interested in participating. There is a Lot of… |
Sequence 3or to have an immediate perception of the difference between two sets-if you want to eat fruit, you need to see what is a… |
Sequence 4In particular, it is evident with PET analysis that correct per- ception of mathematics happens when these two very distant… |
Sequence 5Figure 1. The Montessori number rods. (see Figure 1). Clearly the first way you present the number in Montessori, the number… |
Sequence 6IV.A..,,. J.t JJ.,u,,. ,.U'-' _.., ....,,...,.L ....,. .. .J..-..,_.. ...... 41•.i.,l11.l.t1Jt.d JA,1,,A..._,,1,… |
Sequence 7I really like this because adults tend to forget that "what is necessary is to respect it." Anyway, to me… |
Sequence 8Hence, we have to think that Montessori, who obviously did not know neuroscience, arrived to the same conclusion starting… |
Sequence 9• • • • • • ► ___ ....... .,. ... • • • • • • Figure 7. Even and odd numbers, from Aristotle's Metaphysics. In all… |
Sequence 10As I told you, there are other things Montes- sori observed because she was really a good observer, and they are not yet… |
Sequence 11about the brain. In particular, we know that a newborn has very few synapses. Jn three years, the brain produces an enormous… |
Sequence 12lection. Hence the satisfaction could be an indication of the best activity to suggest in school. Obviously 1 don't want… |
Sequence 13four or five, almost all of them say the left arrives first. The other square appears larger. What we did two years ago with… |
Sequence 14using for pedagogical purposes the history of mathematics. Surely she was a genius. Really she suggested very good acth ities… |
Sequence 1THE ESSENTIAL MONTESSORI MATH THROUGH THE YEARS by John McNamara John McNamara has developed a classical practitioners… |
Sequence 2Here is one of the quotes from Maria Montessori that 1 be- lieve guides me daily in what L do:" Imagination does… |
Sequence 3Then one girl, who, up to this time, would have said she didn't Like math, looked at us and said, "You guys are… |
Sequence 4We've all heard the expression, "If it's worth doing, it's worth doing well." I think it was… |
Sequence 5four hours one will have driven 140 miles; that if peanuts cost 40 cents an ounce and a bag of them costs $2.20 then there… |
Sequence 6ent strategies. If you think of a traditional math class, the teacher gives the lesson, they do a few sample problems together… |
Sequence 7accomplished something, as opposed to a sigh of relief, "I've finally finished." It's that sense… |
Sequence 8principal, I used my principal prerogative and brought the check- erboard home. J said, "Okay, Dorothy, let's… |
Sequence 9to multiply by the reciprocal. Cnnceli11g is another misnomer we often hear in connection with fractions. Be careful of your… |
Sequence 10MENTAL MATH AND NUMBER SENSE I put a lot of emphasis on mental math, estimation, number sense. In {111111111erncy, John… |
Sequence 11call it 11, multiply by two, and that's 211. Add five, and it's 211 + 5. Multiply by five, and it's 1011 + 25.… |
Sequence 12,1nd dt\ idtn~ b, tens, hundreds thousand.., it.., just \\Orking with powers. It lwcomcs a n;itur,11 part ol their learning.… |
Sequence 13shows the hierarchy. It leads to understanding. Other base systems: My students enjoy doing the different charts with the… |
Sequence 14biology, geography. Evolution did not happen apart from the dynam- ics of the earth. Biological time is geological time. The… |
Sequence 15student said, "We have to know the density of blood versus the density of water." They were bringing in… |
Sequence 16Assisi as saying, "Preach the gospel at all times. When necessary, use words." What I try to do is preach… |
Sequence 17involvement with the materials. Students are engaged in an activity that introduces a new concept. We provide the formal name… |
Sequence 18R111RE~(.l'i (,rautn1, C.1millo. "Ch,1i.1etcristic!-> nf thl• C.hild 111 tlw Flln lnlJr) <,lhool… |
Sequence 1A HISTORY APPROACH TO MATHEMATICS FOR THE ADOLESCENT by Michael Waski Miclznel Wnski shows //tat tlte 11tilizatio11 of… |
Sequence 2If we trust the students, we can allow them to take their time, discover formulae, and make connections that will be accurate… |
Sequence 3REVISITING SKILLS This historical approach helps tremendously with one of the big- gest challenges I face, and that is the… |
Sequence 4Students may say they know how to use the quadratic formula, and when questioned, they kind of say the formula somewhat cor-… |
Sequence 5In a very real way, they are following in the footsteps of people who came before them They are working side by side with… |
Sequence 6we can re-create in a shortened form what the great minds of the past have done. The students can re-create the essence of the… |
Sequence 7The Story of '\umbers: \\'e t•xp,rnd on thl' conn•pt of what number is. Ihm do peopll' view n•,1lity? I… |
Sequence 8,rnc1ent langu,,gt'!'-, Wlwn P,1-.rnl first inquired .,bout gc- omctr) (at the age of nine), he\'"… |
Sequence 9Though Euler went blind in 1766, he continued to work, simply keeping track (in his mind) of computations which wou Id fill… |
Sequence 10I/+_-_+_=_-_+_- __ F,1dor llllt yon thl' left ,rnd combine terms where ,1ppropriatt.•. 11 + (c-_)11 = (_-_-d) ·y… |
Sequence 11Now, if we solve for II and v in terms of p, then we know what y is.* Let us now solve this system of equations. Solve (1)… |
Sequence 12Simplify the fractions and substitute back 111 = 111• ,,,= ± ✓=+-- -- 4 -- Solve for II in terms of the positive only.… |
Sequence 13REFERENCES Anecdotage. April 24, 2010 <http:/ /anecdotage.com/>. Beckmann, Petr. A History of Pi. New York: St… |
Sequence 1A MATHEMATICIAN EXPLORES THE GAP BETWEEN STORIES AND STATISTICS, LOGIC, AND LANGUAGE by John Allen Paulos Joltn Allen… |
Sequence 2At his faint chuckle she turned and faced her once beloved uncle. Unceremoniously she ripped the papers from the pocket of… |
Sequence 3deep. f believe this to be so, and because the gap between stories and statistics is a synecdoche for the gap between C.P.… |
Sequence 4the next minute is .92Z" "Exit polls show that four out of five voters in favor of gun control legislation… |
Sequence 5Probability itself is present in such words as c'1a11ce, likelihood, fate, odds, gods, fortune, luck, happe,zstance,… |
Sequence 6STORIES AS CONTEXT FOR STATISTICS Unfortunately, people generally ignore the connections between the formal notions of… |
Sequence 7from police blotter reports, in which case they're likely to be low; or if they come from scientifically controlled… |
Sequence 8matchbox problem, the drunkard's random walks, the Monty Hall problem, the St. Petersburg paradox, the random d1.ord… |
Sequence 9writing teacher's maxim enioms, a story shows rather than tells. Stories usually employ dialogue and other devices and… |
Sequence 10two d1men,ion,-who thl'\ '11 ,·oll• for, whl'thcr they sml,Kl', or "hat brand of soft drink or… |
Sequence 11To tell us anything useful, multiple correlation analysis must be based on a very large number of people and a much, much… |
Sequence 12Recognition of common stereotypes and knowledge of recur- ring stereotyped situations-restaurant behavior, retail purchasing… |
Sequence 13also the definition of the extroverted mathematician. He's the one who looks at your shoes while hes speaking.) The idea… |
Sequence 14influence in the U.S., for example, and that a similar percentage of each group is racist and that the country is both… |
Sequence 15a series of minor personal mishaps and their personal bad luck are merely embellishing a funny story or trying to establish a… |
Sequence 16One consequence of the mistaken belief that coincidences are quite special and almost always significant is their rarity in… |
Sequence 17toward some entity does not affect the validity of a proof involving it or the allowability of substituting equals for equals… |
Sequence 18specific low-level functionary in a nation-x-wide organization, only fifteen percent of whose members have this characteristic… |
Sequence 19tions, specifically probabilistic and statistical ones (and of narratives and informal discourse as well). These applications… |
Sequence 20pens? The answer is that the matriarch's warning will be followed by forty-nine peaceful days and then, on the fiftieth… |
Sequence 21members of a couple signal their intentions to purchase items and their attitudes toward money would fill a small book. The… |
Sequence 1THE CHILD' s CONSTRUCTION OF GEOMETRY IN Psrco-GEOMETRiA by Benedetto Scoppola Begi1111i11g will, Mo11tessoris… |
Sequence 2Hence each child should have a book, and in this book there should be a dictionary of the geometry words that he or she learns… |
Sequence 3course the child should not be afraid to do work for the geometry book; the search for perfection should be not stressful.… |
Sequence 4age \m·\,,1,, th,., is ,1 f,r.,t ,ery important acti, ity that can be lOl- lcdcd in the geometry book. It b also inll•rcsting… |
Sequence 5diagonals and then, placing the compass point in the cente1~ you make four small arcs. Clearly the distance between the center… |
Sequence 67 .:JL,.o/,.,._ J,w,u-· _____________ ,pAAA.il.d l.un .. u,. k.urA.N.LA ------------- .Lu/fl.1 ,:..a,n. mk41".CA… |
Sequence 7Figure 5. The set square and the right angle. -------- Figure 6. Acute and obtuse angles. The NAMTA Journal 191 |
Sequence 8Remember always that all these activities are parallel-or, better, subsequent-to the manipulation of the insets, where the… |
Sequence 9other exercise very useful is to have some written labels, "isosceles triangle," "obtuse-angled… |
Sequence 10Figure 8. Decoration that calls attention to features of a triangle. Another thing that Montessori suggests is to use the… |
Sequence 11Figure 9. Base and vertex of a triangle. Figure 10. Altitude of a triangle. J Figure 11. Perimeter of a triangle. The NAMTA… |
Sequence 12Figure 12. Classification of quadrilaterals. - .... ' ---------i- ...... .,-1 ,d '""'1~.t… |
Sequence 13recording the discoveries made by doing the concrete activities that are recorded in the geometry book. This list by concept… |
Sequence 14The other list is really a dictionary: List B A • acute • altl•rna tl• • altitude • angle • arr H • ba .. e • bist•… |
Sequence 15After the reading Dehaene~ T/ie Number Se11se, I have an under- standing that this is very meaningful and very important… |
Sequence 16Figure 14. Equivalence. 1 2 1 4 Figure 15. Equivalent relationships. 1 'ffi The triangles that you obtain by… |
Sequence 17Figure 16. Equivalent figures from largest to smallest. in the end you can represent this material on paper (two times for… |
Sequence 18Figure 17. A square that is hall the area of the large square. This square, which has a diagonal equal to the edge of the… |
Sequence 19/ Figure 18. A self-similar structure using triangles. Figure 19. A self-similar structure using squares. grows smaller and… |
Sequence 20,------------------------------------- ---- = + Figure 20. The "problem" of a trapeziod as the sum of… |
Sequence 21The choice of problems that Montessori presents is incredibly well done because this new problem is more difficult: While in… |
Sequence 22Figure 24. Constructing a hexagon by starting with an equilateral triangle. = Figure 25. The difference between the hexagons… |
Sequence 23,------- l Figure 26. Two similar hexagons containing similar triangles. bigger hexagon is the original triangle that we… |
Sequence 24Figure 27. The Pythagorean theorem. Figure 28. A self-similar structure constructed of triangles. confused, but it's… |