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After a conference organized by the Ontario Teachers’ Fed- eration which included repre- sentatives of universities, and secondary and school teachers, a committee was set up, of which Mr. Totten was a member. The committee spent a year developing “Mathâ€" ematics 9" the new grade 9 textbook which was authorized for use last year. after having elementary . standard measuring stickâ€"and also become quite careful about how carefully the measuring is done! Basic principles of algebra 'and geometry are inculcated in grade 1 when the children handle three dimensional ob- jects. such as cylinders.‘ cones. etc. and name them. They also study open and closed curves and their properties as been tried out for three years in various places in Ontario. Throughout the trial period,, Mr. Totten stressed that their} main criteria was whether or‘ not teachers wanted to go back to the old way of teaching mathematics after using the new system. Few of them did; In its emphasis on having the child know the joy of discovery and learning by himself, much arithmetic well as perimeter. area and volume. In all of this. the stress is on discovery with the teacher asking artful ques- tions to spark the child. “You can see by the look on their faces when they discover something for themselves" said Mrs. Routledge. Matt Kinnari. who is teach- .ing the new math to five grade ‘7 and 8 classes at McConaghy in primary grades is now done With the use 01' 00‘1' ;school demonstrated some of his methods. orete materials. i Thls was amply demonstrated: Mr. Kinnari showed how the by Mrs. John Routledge Whomnumber line“ is used to 11- teaches grade 1 at E’leasamvmeilustrate addition. subtraction Public School. Said to knowjand multiplication. His num- mOl‘? about the new mathe"ber line was merely a strip of matics than anyone betweenlwhite paper about three inches Toronto and Sudbury, Ml‘S-‘wide by about six feet long. 0n Boutledge has made a study Of‘thjs he could tack strips of It in all grades from 1 l0 13ipaper of different length and and last summer even took adjffel-ent colours. The green course in calculus at the Uni-Ismp was one unit, the blue one, VerSIty of Toronto. the 0D1Yitwice as long as the green. was primary teacher in the class. two units, the yellow strip was In grade 1 Mrs. Routledge three units and the brown one begins dlSCUSSIOHS With theifour. Thus it could be shown children. on “sets” or groupsigraphically that four plus one and their numerousness. suchlis five. etc. as the stars in the sky\ the carsv‘ The number line can be used In a parking 10!. etc. ’tn illustrate subtraction and A small set is illustrated by the moon in the sky. or the number of cars on the super- market parking lot on 8 Mon- day morning, when there are just a few of them. The child- ren are helped to notice howm ever that this few. if parked in their own driveway would be many. New Mathematics Course Sparks Joy Of Discovery Following this type of discussion the children be- gin manipulating objects in sets. Each child has an “arithmetic box" containing disks. cardboard cutouts. blocks or beads and they learn their arithmetic with these and are not disâ€" tracted by fumbling fingers having to print numbers. Printing the numbers is saved for a printing lesson and is not mixed up with arithmetic. For some months the child- ren work onLv with sets of one. two. three or four objects ile- cause they can see these sets without counting. They disâ€" cover that four is greater than three. that three is less than four and so one A set of seven objects is noticed as being made up of sub-sets of four and three. or five and two. Five is seen as made up of a sub-set of three and two. A handful of jacks may be thrown on the floor. The child- ren see how they land and discover their “number stories" in a concrete situation. instead of memorizing a lot of words which may or may not have any real‘ meaning for the indi- vidual child. Subsequently the children are shown that our number system is based on 10. «Each child has bundles. of ten straws. pipe cleaners. or what have you. and learns for instance that 36 is made up of three bundles of tens and six more. Children may be led to see the need for accurate units of measurement by the old bean bag game. When measuring their throws the teacher may use dif~ ferent measures to record var- ious children's throws. When they find the one who made the shorter flu'ow comes up with a higher score they im- mediately see the need of a My... kuo-lv ..- ...-v r E. E. Totten, master mathematics teacher with York Central District High School Board opened the meeting with a brief outline of how and why the new course had developed. There had been many complaints that mathematics was not being taught properly, he said. Children didn’t appear to enjoy it and many teachers were not enthusiastic about it. Employers complained that the young people they hired could add and subtract “but they didn’t get the right answers.” BY MARGARET McLEAN The auditorium of Lillian McConaghy school was completely filled for last week's meeting of the parent teachers auxiliary when three local teachers discussed and demonstrated the new mathematics bemg taught in the public and secondary schools. order for the Fuel Oil that will lick your heating cares whatever the weather . . . and save you $$$, too! 189 CENTRE ST. EAST TU. 4-1313 Now'sfihe Ume to lay in a good suppl} of Dar)" Queen treats Just 89c buxs you 11 Dilly Bars or Sandwiches at ~\I‘our 3196”? Dairy Queen store. Pak for only C.‘ Closing Sunday, Nov. I I83 YONGE STREET NORTH 4 l E Yall us today to place YOUR E u‘der for the Fuel 011 that. 1 xi” Lick your heating cares { :hatever the weather . . . ’ nd save you $$$, too! { RAMER & son 3 THERE. REALLY Is a NO use IN KICKING â€" WHEN YOU CAN GIVE . Tug cow/x Llamas 'THE COLDA GK! 6- 1mg: Si file No“ s the Ilme to 13\ In a ;ood <uppl_of Dan} 'Queen heals Just 89c hmr‘ ; Fractions also become much . easier to grasp by means of the I number line. When the line is divided in half at one point, it is easily shown that the whole iconsists of two halves; then it ld-Iis further divided into quarters. 1e,'the half is seen to consist of Ie-ltwo quarters and the whole of atsifour quarters. By continuing is-‘in this fashion, dividing the line an into smaller and smaller sec- anltions. the children can see for instance that one half and one is‘third equal not only five sixths ofgbut also two fifths. or! Use of the number line also as‘helps children to grasp easfly Going on in this way, the child is helped to see that in. for instance. multiplying 45 by 26. he is really multiplying 120 x 45 and adding 6 x 45. This is in contrast to the old system where the child was taught to multiply first by six and then by two, always remembering to “move the second line over one" before he added the two to get his final answer, but not necessarily knowing why this was done. In all of this. the stress is on discovery with the teacher asking artful ques- tions to spark the child. “You can see by the look on their faces when they discover something for themselves" said Mrs. Routledge. Matt Kinnari. who is teach-.4 ing the new math to five grade 7 and 8 classes at McConaghy school demonstrated some of? his methods. 7 Mr. Kinnari showed how thel "number line" is used to il-' lustrate addition. subtraction1 and multiplication. His num- ber line was merely a strip of‘ white paper about three inches; wide by about six feet long. On this he could tack strips of‘ paper of different length and. different colours. The green] strip was one unit. the blue one,j twice as long as the green. was“ two units, the yellow strip was‘l three units and the brown one four. Thus it could be shown graphically that four plus one is five, etc. The number line can be used to illustrate subtraction and multiplication as well. By usâ€" ing yellow strips of three units each. it could be demonstrated that 2 x 3 plus 3 x 3 equals Dam! *‘ QUEEN RICHMQflD HILL u and one; (Opposite Fairlawn Ave“ “"8 sixthSJ ONE LOCATION ONLY the basic geometricar principle ythat a line is a series‘:‘of points Thus, stress in ‘he course is on the structure and rela- tionship of numberfi and the children are helped to learn the meaning of number facts. “we want to stretch their-minds to; i think" stated Mrs. Routledge.j ’» Any parents having trou- 1 ' ble stretching their' minds 1 in this way were reminded a that the York Central High ! School Board has thought- i fully arranged a night 1,. school course in the' new " mathematics for parents which is being held at Bay- view Secondary School on | Tuesday and Thursday ev- 1 enings. Announcement was also made ~. of an “Open House” t be held' November 2. Parents will be given a general view of the "‘2 school system with a detailed‘ explanation of the curriculum. They will be able to visit class- rooms. compare the children‘s work which will be on display,‘ and follow the work throug each grade and see its contin-j uity. Teachers may also be iii-l terviewed but on general .sub-l :3 jects, not relating to any partic-ll ulal‘ child. Interim reports will be issued: on October 30 assessing each] . child’s progress and giving the} parents an opportunity to ar-a range an interview if desired; E“lull““lllllllllll““11“!“llllllllllllllllllll“IlllIlllllllllllllfllllflllllllll Members of the McConaghy PTA were also invited to atâ€" tend the January'lQ meeting of the Pleasantville Home & School Association when Noel B. Alder, co-ordinator of Oral French in the public schools for the Ontario Department of Ed- ucation will conduct a .demon- Estration lesson in Oral French. time to SIOCK up on fun Elegant. tailored, jaunty, soph- isticated styles fashioned in luxurious furry felts, opulent materials plus our colorful and metallic toned feathers for dressy occasions. You will want several of these chic chapeaux to compliment y o u r fall-winter costumes. Prices from $6.98 to $29.98. BOX (NUMBER) 'THE LIBERAL‘ WANT ADS 63 YONGE ST. S.. 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