Learning Cognitive Styles & Math Teaching PDF

Learning I. Learning and cognitive styles A. Visualizers vs. verbalizers B. Learning math without words II. Learning without reinforcement A. Cognitive maps B. Overjustification effect III.Role of motivation in learning A. Research on expert tutors B. Growth vs. fixed mindset Learning in Visualizers...

Learning I. Learning and cognitive styles A. Visualizers vs. verbalizers B. Learning math without words II. Learning without reinforcement A. Cognitive maps B. Overjustification effect III.Role of motivation in learning A. Research on expert tutors B. Growth vs. fixed mindset Learning in Visualizers vs. Verbalizers Some people tend to be visualizers while others tend to be verbalizers Ø Neural correlates of visual vs. verbal cognitive styles (Kraemer, Rosenberg, & Thompson-Schill et al., 2009) Researchers administered questionnaire to assess whether participants were more visualizers or verbalizers During fMRI imaging session, participants performed a task involving both word-based and picture-based feature matching conditions that were designed to permit the use of either a visual or a verbal processing style ➜ Visualizers showed more activation in fusiform gyrus area associated with processing visual representations ➜ Verbalizers showed more activation in supramarginal gyrus associated with linguistic processing Verbalizer Dimension Visualizer Dimension Aphantasia: Inability to visualize May be congenital or acquired (e.g., brain injury) Some researchers say 2-3% of population may be affected, and many may be unaware of the condition Ø “I thought counting sheep was a metaphor, just like bee’s knees or cat’s pajamas” May be unable to picture loved one’s face or remember directions; even telling someone how their day was can be difficult because they can’t visualize it Ø “It is hard not to feel like a sociopath when you’re lying about how you spent your Monday and you don’t even know why.” When looking at and naming faces, normal regions of brain are active, but when asked to picture people’s faces, facial-recognition brain regions do not become active like they normally would − Aphantasia characterizes only voluntary visualizations; the aphantasiacs were still able to have involuntary visualizations (i.e., dreams) ➜ Suggests that condition may involve neurological deficits between frontal and visual cortex Teaching Math Without Words: A Visual Approach to Learning Math The vast majority of teaching in school is done through words Teacher writes words and says words; students read books with words and are expected to respond to questions with words However, the vast majority of students are not verbal learners 25% of students in California are English language learners An additional 15% have language learning difficulties, such as dyslexia An additional 20% fail language comprehension tests A large portion of remaining student characterize themselves as visual learners There is only a tiny little segment of students for whom current (verbal) teaching methods are a good fit (Matthew Peterson, MIND Research Institute) Language heavy approach to Algebra I and what it does to kids: ☞ So Matthew Peterson developed an interactive software with visual feedback to teach math concepts from pre-K to Algebra I Software approach where you get immediate visual feedback on why your answer is right or wrong: Can clear up many of the mysteries about how and why math works, such as why multiplying two negative numbers results in a positive number: “We’re basically able to boil all math down to how you help a little penguin across the screen.” Ø Research study on implementing software program in 106 schools in Orange County – After one year, program was able to triple rate of growth in math proficiency – Results were replicated in Silicon Valley, Las Vegas, Chicago, and Houston Language-free approach can actually improve language skills Kids play active role in figuring things out This sparks mathematical talk Ø Ex: Case of student with autism spectrum disorder who only spoke in single words, and rarely spoke those even to parents − When he began the new math software program, he started talking − First full sentence he ever spoke was about mathematical ideas he was experiencing in these visual games − As a result, he started excelling in school in both math and English – program completely transformed his life Learning without Reinforcement According to behaviorist theory, the consequences of a response (i.e., reward or punishment) will increase or decrease the likelihood that a response will occur again However, outcomes not always what would be predicted by strict behaviorist theory: learning is not just a matter of acquiring stimulusresponse associations, but must take into account the mental processes of the organism, such as its interpretation of the stimulus Ø Ex: Edward Tolman’s experiments on cognitive mapping in rats (1930) − Experiments with maze learning in rats showed that learning can occur even when 1) No reinforcement is received and 2) No response is made Ø Research on the overjustification effect − Children who had been offered reward for playing with special magic markers were later less likely to play with the markers during free play Good Player ➔They came to view the activity as work rather than as play ☞ Rewards can undermine motivation (Lepper, Greene, & Nisbett, 1973) − Another example of rewards undermining intrinsic motivation o Dating couples were asked to think of either the extrinsic rewards (“s/he knows a lot of people”) or the intrinsic rewards (“we always have a good time together”) they obtained from going out with their partners ➔ Couples who had thought about extrinsic rewards later evaluated themselves as being less in love Role of Motivation in Learning Studies of expert tutors found that these tutors will do anything to avoid telling a child that he is wrong – even to the point of lying! ☞ Tutoring – and learning – is 90% motivational (Lepper & Woolverton, 2001) Ø To teach child to read, need to find subject that child is interested in (e.g., sports magazines) Growth vs. Fixed Mindset Underlying assumption of IQ tests that intelligence is innate and fixed undermines motivation – and learning Ø Research by Dweck and Blackwell (2007) on students who were predominantly minority and low achieving Control group was taught study skills Experimental group got study skills and a special module on how intelligence can be improved that was taught in two lessons totaling 50 minutes ➜ Those who got the special module showed dramatic improvement in study skills and grades - They pushed themselves harder - They tried new things ☞ This very brief intervention basically reversed the students’ longtime trend of decreasing academic scores v The kids who had cultural reasons to be anxious about their skills were the ones most affected by the message, e.g., girls and math Recent research has found that Programs to develop growth mindset are most beneficial in students with low socioeconomic status or who are academically at risk (Sisk, Burgoyne, Sun et al., 2018) Low income students are less likely to hold a growth mindset than their wealthier peers ➜ However, low income students who exhibit a growth mindset show academic performance as high as that of fixed mindset students from higher income brackets (Claro, Paunescu, & Dweck, 2016) Video References Videos excerpted from: Teaching without words: Matthew Peterson, TEDxOrangeCoast https://www.youtube.com/watch?v=2VLje8QRrwg