5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL March 12-14 ictcm.com | #ICTCM 1 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM Helping Students Maintain Calculus Skills over School Breaks 2 1
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM Carla van de Sande Associate Professor of Mathematics Education Arizona State University carla.vandesande@asu.edu 3 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM If you don’t use it, you lose it… • Not just physical skills…cognitive skills too! (Cooper, 2003) • A real problem for K-12 students (Cooper, Nye, Charlton, Lindsay, & Greathouse, 1996) 4 2
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM • Hurts math learning especially. (Cooper, 1989) • Extends even beyond K-12 … (van de Sande & Reiser, 2018) 5 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM Why does it matter? COURSE 2 Z x ln x dx = ? NEW MATERIAL Z Z Course 2: u dv = uv − u dv Integration by parts u = ln x dv = x dx Course 1: du = 1 v = 1 Course 1: Derivative of 2 x 2 xdx Antiderivatives natural log (power rule) function Z 1 = 1 2 x 2 ln x − 2 x dx Course 1: = 1 2 x 2 ln x − 1 Course 1: 4 x 2 + C Antiderivatives COURSE 1 Indefinite (power rule and integrals factor) PRIOR MATERIAL 6 3
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM How can we help them remember? Retrieval practice and the Testing Effect (Butler, Marsh, Slavinsky, & Baraniuk, 2014; McDaniel, Anderson, Derbish, & Morrisette, 2007; Roediger & Butler, 2011; Roediger & Karpicke, 2006) . “Nudges ” (Castleman & Meyer, 2016; Castleman & Page, 2013, 2014; Karlan et al, 2010; Obermayer, Riley, Asif, and Jean-Mary, 2004; Kraft & Dougherty, 2013; Thaler & Sunstein, 2008; Woolford, Clark, Strecher, & Resnicow, 2010; Kraft & Monti-Nussbaum, 2017) . 7 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM K SS A program to K eep i n S chool S hape during breaks in traditional instruction 8 4
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM 9 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM I donated to the cause that got the most correct answers. 10 5
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM Daily problems were designed and delivered using Qualtrics TM survey software Before solving the problem, they rated their confidence. 11 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM Right or wrong, they could choose to see the solution or finish If they got the daily KiSS problem right, they selected a charity 12 6
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM PARTICIPATION Amounts and Patterns 13 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM How many ASU students participated? 269 students signed up and 213 did at least one problem Participation by Day 120 100 Number of Students 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 KiSS Problem # 14 7
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM No problems 4% 21 – 25 problems 32% 1 – 5 problems 24% 6 – 10 problems 13% 16 – 20 problems 17% 11 – 15 problems 9% 15 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM When did the “one shot” students participate? …at the start of the KiSS program 16 8
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM When and how did the “give it a try” students participate? …mostly during the first week of the KiSS program M T W TH F Sa Su M T Th F Sa Su M T Th F Sa Su M T W Th F Sa 16th 17th 18th 19th 20th 21st 22nd 23rd 24th 26th 27th 28th 29th 30th 31st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 n student V Coyo Hatsune Miku False Crown Emmy DNL Hunty CoolMathGames Maitreya Sterling Archer AngelJ LMPM Saac Jim Daylight Sunistatic Butroz Q Steel Blizz Meow Esteban Wild-rose S Mr. Sunil Aedan Frodo Anthony aslyons04 iceBerglettuce Andrew2 Sageboi CrimsonKg.ASU Ginger386 Ruan 17 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM When and how did the “half in” students participate? …large clusters of days throughout the KiSS program M T W TH F Sa Su M T Th F Sa Su M T Th F Sa Su M T W Th F Sa 22n 26t 27t 28t 29t 30t 16th17th18th19th20th21st d 23rd24th h h h h h 31st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th11th 1 2 3 4 5 6 7 8 9 ## ## ## ## ## 15 ## ## ## ## ## ## ## ## ## ## n student V Renevaine Silver tingling Unicornwolf01 Kian12313 Everest S AZM S Aaron S Goonga Ginga B_hm Winters kateri KBHB Varsh TB12 Shah J49 MAT 266 Dev Mat266 Jake H 18 9
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM CONFIDENCE AND ACCURACY Level of difficulty 19 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM 20 10
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM How did they do? Students found some of these fundamental problems difficult. Percent of Students Who Answered Correctly 100 90 80 70 60 % Correct 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 KiSS Problem # 21 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM 22 11
5/4/20 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM Who looked at the solutions? Almost all after getting it wrong and 30% after it right. Viewing Solution by Accuracy 100% 90% No thanks 80% 70% Got it right Show me Got it wrong 60% 50% 40% 30% 20% Show me 10% 0% 23 32 nd International Conference on Technology in Collegiate Mathematics ORLANDO, FL | MARCH 12-14 #ICTCM KiSS Program Highlights What did we learn? • Well received • Cost-effective • Informative • Adaptive 24 12
5/4/20 K SS … EVEN DURING BREAKS FROM SCHOOL Carla van de Sande Associate Professor of Mathematics Education Arizona State University carla.vandesande@asu.edu 25 13
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