C82LEA Biology of learning and memory Number. What abilities are involved in numerical competence? 1) Relative numerosity discrimination 2) Absolute

  • View
    214

  • Download
    1

Embed Size (px)

Text of C82LEA Biology of learning and memory Number. What abilities are involved in numerical competence?...

  • Slide 1

C82LEA Biology of learning and memory Number Slide 2 Slide 3 What abilities are involved in numerical competence? 1) Relative numerosity discrimination 2) Absolute number discrimination 3) Ability to count 4) Ability to do arithmetic Slide 4 1) Relative numerosity discrimination The ability to discriminate between sets of items on the basis of the relative number of items that they contain. First to try was Koehler c. 1913 Emmerton, Lohmann & Niemann 1997 manyfew trained pigeons to discriminate between "few" (1/2 items) and "many" (6/7 items) Slide 5 few many Slide 6 few many.. but are the birds ignoring number, and instead using some other feature of the display? eg light=few dark=many Slide 7 few many.. but are the birds ignoring now DARK=few and LIGHT = many Slide 8 3 4 5 how well do they transfer to new numbers? if they really understand few versus many, they should... Slide 9 1/2 3 4 5 6/7 novel displays Slide 10 2) Concept of absolute number understanding that 4 bananas and 4 elephants have something in common...... i.e. number is not intrinsically related to what you are counting Slide 11 Koehler again... Jakob the raven could choose a pot with five spots from an array, even when size of spots varied 50-fold Matsuzawa (1985): chimp called Ai had to select one of six response keys (labelled 1-6) when shown arrays of red pencils, with 1-6 pencils per array. Achieved > 90% accuracy. 1 23456 1 4 Slide 12 But this is not necessarily the same as counting.... Animals could be learning about specific perceptual pattern -- perceptual matching. Slide 13 But this is not necessarily the same as counting.... Animals could be learning about specific perceptual pattern -- perceptual matching. Argued no, as Ai could transfer her ability to arrays of different types of item 4 Slide 14 Slide 15 the perceptual matching problem... often number is confounded with other factors such as time (for items presented serially) and space (for items presented simultaneously). Are animals using number or these other cues? e.g. smaller number of items also takes up less space. Is it the size of the display controls the response, not number ?? Slide 16 with visual arrays there is always going to be something.. so hard to rule out but people have tried in various ways e.g. Pepperberg, 1994 Slide 17 Sample of Trials 1. 1 orange chalk, 2 orange wood, 4 purple wood, 5 purple chalk How many purple wood? (4) 2. 1 yellow block, 2 gray block, 4 yellow wool, 6 gray wool How many yellow block? (1) 3. 1 rose wood, 2 blue nail, 3 blue wood, 5 rose nail How many rose nail? (5) Slide 18 Sample of Trials 4. 2 gray truck, 3 gray key, 4 orange key, 5 orange truck How many gray key? (3) 5. 1 blue box, 3 green box, 4 blue cup, 6 green cup How many green cup? (6) 6. 1 purple rock, 2 green rock, 3 purple plastic key, 4 green plastic key How many green rock? (2) Slide 19 another perceptual matching argument... Are the animals subitising? The perception at a glance of the number of items present, without counting them successively; the maximum number of items that can be counted in this way is five Slide 20 Slide 21 HOW MANY? Slide 22 Slide 23 Slide 24 The original claim was that subitizing is different from counting because there is little increase in reaction time per item for low numbers of items whereas when dealing with numbers bigger than six, you have to count each one, and because it takes a finite amount of time to count each item the RT increases with number of items This implies that you do not need to count displays of five items or less -- the number is perceived immediately But is this true? Slide 25 However, there is an effect of display size with displays of less than five items -- it takes longer to perceive twoness than oneness, and so on This suggests that even with small displays we are using a counting process Slide 26 Meck and Church (1983): serially presented items. Rats trained with two signals 2 or 8 pulses of white noise. after 2 were rewarded for left lever response after 8 rewarded for right lever response Respond LEFTRespond RIGHT Each pulse 0.5 sec -- 2 pulse lasted for 2 seconds, 8 pulse for eight seconds. Were animals were responding on the basis of the total time, not number of pulses? Slide 27 To investigate this, they devised a test in which both stimuli lasted 4 seconds: Respond LEFTRespond RIGHT If rats were responding on the basis of stimulus duration, this task should be impossible but they continued to respond correctly Slide 28 To investigate this, they devised a test in which both stimuli lasted 4 seconds: Respond LEFTRespond RIGHT The rats were also tested with pulses of light -- and continued to respond appropriately (Church & Meck, 1984). This is more evidence against perceptual matching Can you think of any other confounds? Slide 29 .. or can make animal respond a fixed number of times no array involved Davis & Bradford (1991) Access to a plank with food pellets on it Experimenter nearby talking to rat Each rat had designated number of pellets to eat if he ate more the experimenter shouted No! or clapped loudly. When they ate the right number or fewer than the target they were rewarded by praise and petting (and also a little more food) got it right even when no longer rewarded for correct responses transferred to sunflower seeds - Slide 30 Further evidence from Capaldi & Miller, 1988 Rats trained in a runway, sometimes with food at the end. If the rats expect food they run fast! Trained with following sequences of reinforced (R) trials and nonreinforced (N) trials -- RRRN and NRRRN. Learn to anticipate final N trial and run slow.... Slide 31 N R R R N after extensive training.... NRRRN trial... and on an RRRN trial Slide 32 R R R N after extensive training.... NRRRN trial... and on an RRRN trial Slide 33 Learning that three rewards mean no more...? not e.g. length of time in apparatus...... and were trained with rat pellets; but if one or more of the rewards in the sequence were changed to, for example, cocoa pops, they still did well Slide 34 What abilities are involved in numerical competence? 3) Ability to count Gelman & Gallistel (1978) argued that counting involves mapping numerosity (the property of the display -- e.g. two items) onto a label that represents that numerosity. We usually use number words or symbols as labels, but presumably animals use nonverbal labels, which we can call numerons. Slide 35 The process of counting involves three principles: i) one-to-one principle: each item is assigned only one numeron 14 = 4!! 32 Slide 36 The process of counting involves three principles: i) one-to-one principle: each item is assigned only one numeron ii) stable-order principle: numerons must always be assigned in the same order 14 31 2 = 4!! 32 = 2!! Slide 37 The process of counting involves three principles: i) one-to-one principle: each item is assigned only one numeron ii) stable-order principle: numerons must always be assigned in the same order iii) cardinal principle: the final numeron assigned applies to the whole display 14 31 2 231 = 4!! 32 = 1!! = 2!! Slide 38 Not just about knowing correct number labels Implies knowledge about order of these labels e.g. 1 2 3 4..about how these labels are ordered in relation to quantity e.g. 4>3 2>1 --- ordinal scale and that the size of the difference between each item is the same e.g. 4-3= 3-2 --- interval scale Slide 39 Representation of number in the chimpanzee? Biro & Matsuzawa 2000 Ai trained to touch arabic numerals in ascending order Slide 40 Representation of number in the chimpanzee? Biro & Matsuzawa 2000 Ai trained to touch arabic numerals in ascending order But some argued that it was just rote learning of a particular stimulus-response sequence... - no requirement to know anything about the quantitative relation between numbers Slide 41 Representation of number in the chimpanzee? Brannon & Terrace, 2000 Chimps (Benedict, Rosencrantz & MacDuff) trained to order arrays of 1-4 items in ascending, descending, or random order same sizesame surface areavary sizeclip art Slide 42 Representation of number in the chimpanzee? Brannon & Terrace, 2000 Chimps (Benedict, Rosencrantz & MacDuff) trained to order arrays of 1-4 items in ascending, descending, or random order same sizesame surface areavary sizeclip art mixed clip artvary size and shapevary size, shape, colour Slide 43 They could learn ascending and descending orders, but not the arbitrary order 1-3-2-4 Representation of number in the chimpanzee? Brannon & Terrace, 2000 Chimps (Benedict, Rosencrantz & MacDuff) trained to order arrays of 1-4 items in ascending, descending, or random order Slide 44 Representation of number in the chimpanzee? Brannon & Terrace, 2000 Then they were tested with novel displays of 5-9 items 86 75 Slide 45 The chimps taught an ascending order could generalize immediately to the higher numbers.... but those taught a descending order could only generalize after further training 86 75 implies (limited) understanding of the ordering of quantities Slide 46 Alex again... (Pepperberg, 2000) 1 orange chalk, 2 orange wood, 4 purple wood, 5 purple chalk How many purple wood? (4) Slide 47 Alex again... Slide 48 4) Ability to do arithmetic To perform the operations of addition, subtraction etc. To some extent this can be done by rote learning (e.g. times tables); but true mathematical competence would allow these operations to be generalised to new situations in a way that implies a concept of number. Slide 49 4) Ability to do arithmetic To perform the operations of addition, subtraction etc. To some extent this can be done by rote learning (e.g. times tables); but true mathematical competence would allow these operations to be generalised to new situations in a way that implies a concept of number. It is worth asking yourself exactly what