6_1 : Kapur Productive Failure In Learning Math Flashcards
What are the key concepts in what we read?
- Productive failure
- Direct Instruction
- Vicarious failure
Productive Failure
engage students in problem-solving first and then teach them the concept and procedures
Benefits of productive failure
- Failing can prepare students to learn better from subsequent discussion
- Good for activating prior knowledge
- Difficulties might aid encoding and prepare Ss to learn
- improved sense of agency (motivating) “i know we haven’t learned this yet but you will get it!”
- good for metacognition (see limits of own knowledge)
- Opportunities to compare student-generated solutions to “correct solutions”
Direct instruction
sequence of instruction followed by problem-solving
Benefits of direct instruction
- reduces the probability of encoding errors/misconceptions
- Ss may not otherwise discover knowledge on their own
- All working memory is available for learning (if you’re too busy trying to find the correct answer, then you aren’t paying attention, DI allows you to only learn)
- Might reduce frustration
What question(s) did the author(s) set out to answer?
Which is a better way to teach (math)?
- teach concepts/procedures → solve problems: directive instruction
- Solve problems →(failure)→ teach concepts/procedures: productive failure
Study 2:
- evaluate problems →(see failure)→ teach concepts/procedures: vicarious failure
How did the author(s) go about studying their research question(s)? - Study 1
2 randomized control trials (takes care of factors not under experimental control randomizes variation)
Study 1 - DI VS PF
N= 75 9th graders in India
- ## no prior instruction in Standard deviation
Measured math ability**
- Pretest related to basic statistics
- ## math standardized test scores
Random assignment to 2 conditions w/ 2 phases : same teacher in both conditions; blind to hypothesis
- DI: 1 hr instruction → 1 hr problem solving
- ## PF: 1 hr problem solving → 1 hr instruction
During instruction (for both groups)
- Teacher taught concept and procedure for standard deviation
- 4 problems
- each/ T modeled, S practiced, S got feedback
- T highlighted critical features and common misconceptions
- ## DV: performance on the 4th problem
Problem-solving phase (both groups)
- math problems on SD, multiple solution strategies
- worked individually, w/o help
- Task: generate as many solutions as possible
- ## DV: # of solutions
more DV
-
After each phase students rated -
- engagement (5 items, likert scale)
- mental effort (2 items, likert scales)
- ## Each S had 2 composite scores for engagement and 2 composite scores for mental effort
Post-test
- After 2nd phase
- 40 minutes
- targeted
- procedural knowledge (compute & interpret SD)
- conceptual understanding (critical features of SD)
- transfer (to topic of normalization)
How did the author(s) go about studying their research question(s)? - Study 2
Method**
N = 111 9th graders in India
Random assignment 2 conditions w/ 2 phases : same teacher in both conditions; blind to hypothesis
- DI: 1 hr instruction → 1 hr problem solving
- PF: 1 hr problem solving → 1 hr instruction
- VF: 1 hr evaluate solutions → 1 hr instruction
Benefits of VF
- Not having to generate solutions frees up working memory for encoding
- neither group has necessary domain knowledge to solve the problem. So VF Ss may benefit more from evaluating than PF from generating
What did they find Study 1
Overall
- PF Ss reported working harder
- PF Ss outperformed DI Ss on conceptual understanding and transfer w/o compromising procedural knowledge
- PF Ss # of solutions was correlated w/ conceptual understanding and transfer performance
- ## PF method seemed to activate prior knowledge and prepare them to learnResults: group difference in math ability**
- Pretest related to basic stas: n.s.
- math standardized test scores: n.s.
Results: instruction phase (DI 1st, PF 2nd)
Percent correct on 4th problems
- DI Ss: 97.4%
- PF Ss: 97.3%
Results: Problem solving phase**
DI Ss
- Produced ~ 3 solutions on average
- all produced the canonical (i.e. standard solution)
- Used what they were taught + 2 solutions
PF Ss
- Produced ~ 6 solutions on average
- none produced the canonical solution
Results: Effort & Engagement**
- Mental effort: PF > DF during problem-solving & instruction
- engagement: n.s.
Result:posttest scores**
- Procedural knowledge: PF = DI
- Conceptual knowledge: PF > DI
- Transfer: PF>DI
PF did better on a deeper understanding of knowledge
- within PF condition
- the more solutions strategies, the better conceptual and transfer knowledge they acquired for the post-test
What did they find - Study 2?
OVERALL STUDY 1 & 2
- PF & VF > DI - struggling is good, especially on your own
- PF > VF - generating is better than evaluating
- Helping to produce correct solutions may constrain the search for new solutions
Results : group difference in math ability
- Pretest related to basic stas: n.s.
- math standardized test scores: n.s.
Results: instruction phase (DI 1st, PF 2nd, VF 2nd )
Percent correct on 4th problems
- DI Ss: 97.4%
- PF Ss: 94.7%
- VF Ss: 94.7%
Results: Problem solving phase
DI Ss
- Produced ~ 3 solutions on average
- all produced the canonical (i.e. standard solution)
- Used what they were taught + 2 solutions
PF Ss
- Produced ~ 6 solutions on average
- none produced the canonical solution
Results: Effort & Engagement
-
Mental effort:
- Instruction phase: PF >VF> DF
- problem-solving/evaluation : PF>VF & DI
- Engagement: n.s.
Result:posttest scores
- Procedural knowledge: n.s
-
Conceptual and trasnfer
- PF > VF & DI on conceptual understanding and transfer (PF stood out and did the best overall)
- VF > DI on conceptual understanding
- # of solutions generated y PF Ss during problem-solving was correlated with their posttest score on conceptual understanding and trasnfer
PF did better on a deeper understanding of knowledge
Why should we care?
Helpful when we learn new topics and how we can teach new topics
