WEBVTT 1 00:00:00.010 --> 00:00:02.959 So welcome to this video with the last 2 00:00:02.959 --> 00:00:06.330 important concept, pedagogical concept. 3 00:00:06.330 --> 00:00:08.849 But you will actually notice, as we've 4 00:00:08.849 --> 00:00:10.860 done in previous videos, that there is 5 00:00:10.860 --> 00:00:13.130 quite some overlap because there is a an 6 00:00:13.130 --> 00:00:16.529 integrated vision you could say in Asia 7 00:00:16.529 --> 00:00:20.100 on mathematics. This one is about how 8 00:00:20.100 --> 00:00:23.840 'practice makes perfect' and how actually, 9 00:00:23.840 --> 00:00:26.420 like The Two Basics, 10 00:00:26.420 --> 00:00:29.160 procedures and algorithms go hand in 11 00:00:29.160 --> 00:00:31.230 hand with conceptual understanding. 12 00:00:31.230 --> 00:00:33.719 I hope you realise that in all these 13 00:00:33.719 --> 00:00:36.390 videos this was a theme: in Variation 14 00:00:36.390 --> 00:00:39.719 Theory it was important that procedures 15 00:00:39.719 --> 00:00:42.780 and understanding went hand-in-hand in 16 00:00:42.780 --> 00:00:45.090 the way that tasks were designed. In the 17 00:00:45.090 --> 00:00:47.760 Two Basics it was important that both 18 00:00:47.760 --> 00:00:50.670 went hand-in-hand as well. In the 19 00:00:50.670 --> 00:00:53.219 concrete-pictorial-abstract approach on 20 00:00:53.219 --> 00:00:55.530 the one hand you had the concrete aspect 21 00:00:55.530 --> 00:00:58.230 on the other hand you had the abstract 22 00:00:58.230 --> 00:01:01.050 approach, so these things really go very 23 00:01:01.050 --> 00:01:04.080 much hand-in-hand. That already indicates 24 00:01:04.080 --> 00:01:07.500 that practice is deemed quite important 25 00:01:07.500 --> 00:01:11.159 in China and actually in Asia. 26 00:01:11.159 --> 00:01:13.890 Also recall the statements from a previous 27 00:01:13.890 --> 00:01:16.530 video from Chinese traditional culture 28 00:01:16.530 --> 00:01:19.619 'practice makes perfect', 'while learning 29 00:01:19.619 --> 00:01:23.340 the exhilaration' or 'gain new insights 30 00:01:23.340 --> 00:01:27.180 through reviewing old material'. 31 00:01:27.180 --> 00:01:29.790 We covered for example the article by 32 00:01:29.790 --> 00:01:31.979 Rittle-Johnson, Siegler and Alibali 33 00:01:31.979 --> 00:01:35.220 where there was an iterative relation 34 00:01:35.220 --> 00:01:37.229 between conceptual understanding and 35 00:01:37.229 --> 00:01:40.259 procedural skills. They go hand-in-hand. 36 00:01:40.259 --> 00:01:43.200 A review of the empirical evidence in 37 00:01:43.200 --> 00:01:46.079 that article showed that mathematics 38 00:01:46.079 --> 00:01:48.479 learning indicates that procedural 39 00:01:48.479 --> 00:01:50.130 knowledge supports conceptual knowledge 40 00:01:50.130 --> 00:01:52.470 as well as vice-versa and thus that the 41 00:01:52.470 --> 00:01:54.299 relations between the two types of 42 00:01:54.299 --> 00:01:56.820 knowledge are bi-directional. But they 43 00:01:56.820 --> 00:01:59.250 also said that the order of these two 44 00:01:59.250 --> 00:02:03.240 things was not the most important thing 45 00:02:03.240 --> 00:02:04.920 and actually that there wasn't much 46 00:02:04.920 --> 00:02:07.170 research on this. When you really say 47 00:02:07.170 --> 00:02:09.660 they go hand-in-hand they go hand-in-hand. 48 00:02:09.660 --> 00:02:12.520 Both are equally important. 49 00:02:12.520 --> 00:02:14.560 There are more sources that say that 50 00:02:14.560 --> 00:02:17.320 practice is important. Perhaps you've 51 00:02:17.320 --> 00:02:20.170 heard the work from Anders Ericsson. He 52 00:02:20.170 --> 00:02:24.580 is an expert on expertise; he's an expert 53 00:02:24.580 --> 00:02:25.480 on experts. 54 00:02:25.480 --> 00:02:29.290 He studied elite experts: musicians, chess 55 00:02:29.290 --> 00:02:32.710 players to see how they became experts. 56 00:02:32.710 --> 00:02:36.130 And his conclusion was that they all 57 00:02:36.130 --> 00:02:38.770 practice something called 'deliberate 58 00:02:38.770 --> 00:02:41.620 practice': they were practicing with a 59 00:02:41.620 --> 00:02:44.260 certain focus and they kept on 60 00:02:44.260 --> 00:02:46.630 practicing and by doing that they became 61 00:02:46.630 --> 00:02:49.150 more and more expert. Another important 62 00:02:49.150 --> 00:02:52.030 result in psychology is the testing 63 00:02:52.030 --> 00:02:54.490 effect or sometimes known as retrieval 64 00:02:54.490 --> 00:02:57.490 practice. The testing effect is the 65 00:02:57.490 --> 00:02:59.350 finding that long-term memory is 66 00:02:59.350 --> 00:03:01.360 increased when some of the learning 67 00:03:01.360 --> 00:03:04.000 period is devoted to retrieving the 68 00:03:04.000 --> 00:03:06.220 to-be-remembered information through 69 00:03:06.220 --> 00:03:09.520 testing with proper feedback. I know that 70 00:03:09.520 --> 00:03:11.950 testing sometimes has had a negative 71 00:03:11.950 --> 00:03:15.630 connotation but if you do it well, 72 00:03:15.630 --> 00:03:18.550 testing can actually help your learning. 73 00:03:18.550 --> 00:03:20.920 Especially if you then get feedback on 74 00:03:20.920 --> 00:03:24.250 how you did and you can improve this. 75 00:03:24.250 --> 00:03:27.220 The effect is also sometimes called, as I 76 00:03:27.220 --> 00:03:29.830 mentioned before, retrieval practice. So 77 00:03:29.830 --> 00:03:31.810 it already has the word practice in it. 78 00:03:31.810 --> 00:03:35.380 Or sometimes practice testing or test 79 00:03:35.380 --> 00:03:38.260 enhanced learning. Although this is a 80 00:03:38.260 --> 00:03:41.650 secondary example, I have seen this in my 81 00:03:41.650 --> 00:03:43.990 own research as well. Here you can see an 82 00:03:43.990 --> 00:03:45.760 example from my own research in 83 00:03:45.760 --> 00:03:48.490 secondary mathematics where repeated 84 00:03:48.490 --> 00:03:52.030 practice of solving equations at home in 85 00:03:52.030 --> 00:03:54.940 an online technological environment, with 86 00:03:54.940 --> 00:03:57.280 numbers that kept on changing, were 87 00:03:57.280 --> 00:04:00.580 randomised, with some feedback as you can 88 00:04:00.580 --> 00:04:04.240 see here. If you made a mistake or you 89 00:04:04.240 --> 00:04:07.030 needed a hint, contributed to increased 90 00:04:07.030 --> 00:04:09.580 skills and understanding. So again, 91 00:04:09.580 --> 00:04:12.720 retrieval practice, testing effect, 92 00:04:12.720 --> 00:04:15.700 'practice makes perfect'! Like all other 93 00:04:15.700 --> 00:04:18.160 Asian principles we conclude that 94 00:04:18.160 --> 00:04:19.750 practice is essential in good 95 00:04:19.750 --> 00:04:22.210 mathematics education, both procedural 96 00:04:22.210 --> 00:04:25.320 fluency, so practice and skills, 97 00:04:25.320 --> 00:04:28.200 and conceptual understanding mutually 98 00:04:28.200 --> 00:04:31.260 reinforce each other. So you get the best 99 00:04:31.260 --> 00:04:34.000 of both worlds.