Uncertainty
How did the three conditions rank relative to each other in terms of curiosity level measured?
BONUS: Did the results match what the researchers hypothesized?
1. Unexpected Uncertainty (UU)
2. Expected Uncertainty (EU)
3. No Uncertainty (NU)
BONUS: No - researchers thought results would be [UU = EU > NU] not [UU > EU > NU]
What is the difference between Wait Time 1 and Wait Time 2?
Wait Time 1: Wait time after a teacher finishes asking a question
Wait Time 2: Wait time after a student finishes answering a question
What similarities were found to be present in all countries examined in study?
1) Teachers did majority of the talking (8:1 ratio of teacher words to student words)
2) All teachers taught math using a mix of whole-class discussion and individual work
3) Majority of math was taught by working on math problems (at least 80% of the time)
What made the US Air Force Academy such an ideal setting for a study looking at the impact of Professor quality? Name at least 3 qualities.
1) Students were required to take a very broad range of common core courses w/ equally "predictable" subsequent courses
2) The Math Department split grading equally amongst all faculty; professors teaching the same course would collectively grade all students' assignments together
3) All faculty teaching the same course would use very similar syllabi
4) Tests and exams were given at similar "testing seasons" & all students would be administered similar tests
5) During the testing period of the study, no assignments were given that were "professor or class specific" so the assignments that comprised the final earned grade were consistent
6) Students couldn't choose professors or classes; the academy would randomize students by virtue of this
Did the Math Anxiety study test girls/students' anxiety?
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How did the three conditions differ in levels of learning and transfer?
BONUS: What factor did the researchers think would cause there to be differences in levels of transfer between Unexpected Uncertainty & Expected Uncertainty?
Learning: [UU = EU = NU]
Transfer: [UU = EU > NU]
BONUS: Researchers thought lesser negative affect in EU would lead to greater transfer compared to UU.
What was the purpose of each of the two experiments conducted in the Gaze Aversion study?
BONUS: What was the major finding of Experiment 2?
Experiment 1's goal was to see if Gaze Aversion could be taught.
Experiment 2's goal was to see if Gaze Aversion developed naturally in a child's first year of primary school.
BONUS: GA develops naturally, with substantial acquisition occurring in GA even without training in five year-olds.
Name at least 2 differences in mathematical teaching that exists between High Achieving Countries
1) Time spent per math problem ; Japan stood out for spending on average 15min/problem. Other countries in the study spent anywhere from 2-5 min on average per problem.
2) Emphasis on problems using "real-life contexts" ; the Netherlands and Japan were polar opposites when it came to this feature of mathematical teaching
3) Time spent on "types of math problems": using procedures, stating concepts, and making concepts.
4) Time spent reviewing old content versus working through new content
How did student predictions of their performance in the instructor fluency study align or misalign with their actual performance? State the condition and then the results afterwards.
BONUS: How did the scores of the conditions compare between each other?
1) Fluent condition: Students vastly overrated their predicted performance. Their actual performance fell significantly below that of their predictions.
2) Disfluent condition: Students' predictions and actual scores were not statistically dissimilar.
BONUS: Both groups scored similarly on the memory test afterwards. This means that not only did the fluent condition severely overrate their performance, but also that fluency doesn't translate to greater performance.
What college major displays the highest math anxiety? What was the age group of girls in the math anxiety study and why is that important?
Elementary education majors display the highest level of math anxiety.
The girls in the math anxiety study were in first and second grade. This early in life, young children are particularly sensitive to the role modeling of those of the same gender.
Why should we care about this study and its results?
1) Uncertainty was shown to have a causal and significant impact on transfer.
2) Expectation was shown to have buffered against negative affect, with Expected Uncertainty (EU) inducing the same level of transfer as Unexpected Uncertainty (UU) while experiencing lower levels of negative affect.
Name at least 4 observed benefits of increased wait time.
1) The length of student responses increases between 300% and 700%, in some cases more, depending on the study.
2) More inferences are supported by evidence and logical argument.
3) The incidence of speculative thinking increases.
4) The number of questions asked by students increases, and the number of experiments they propose increases.
5) Student-student exchanges increase; teacher-centered "show and tell" behavior decreases
6) Failure to respond decreases
7) Disciplinary moves decrease
8) The variety of students participating voluntarily in discussions increases. Also, the number of unsolicited, but appropriate, contributions by students increases
9) Student confidence, as reflected in fewer inflected responses, increases.
10) Achievement improves on written measures where the items are cognitively complex
State and provide an example of each of the different types of math problems.
1) Using Procedures:
Ex: "Graph y = 2x + 7"
2) Stating Concepts:
Ex: "Find the y-intercept"
3) Making connections:
Ex: "Graph y = 3x + 4 and 2y = 4x + 2. How does the slope affect the shape of the lines and determine whether or not the lines intersect?"
How did conditions in the professorial fluency study impact the participants' desire and motivation to study?
BONUS: What are the implications of this study as a whole?
It didn't - both groups studied for roughly the same amount and scored similarly on the test.
BONUS: Students' need to be able to accurately predict their performance and knowledge of content. If instructor fluency leads there to be gaps between perception and reality, that hinders students' ability to improve and confront their weaknesses.
What were the three (four technically) experiments conducted in the test anxiety paper? What purpose did each of the three serve?
BONUS: How did the control group compared to the treatment group in lab studies #1 and #2?
Lab Study #1: Looked at whether expressive writing intervention was effective in buffering against test anxiety.
Lab Study #2: Looked at whether expressive writing was actually necessary for that buffering effect to be observed or if unrelated writing would also produce similar results.
Field Experiments #3/#4: Repeated experiments from the Lab in an actual high school right before finals. Meant to see if the EW intervention would be effective in real world settings.
BONUS: The control group performed worse on the post-test than pre-test. The EW group performed significantly better on the post-test than the pre-test.
How was affect, both positive and negative, shown to predict learning and transfer?
Positive affect positively predicted learning ONLY but not transfer
Negative affect was shown to not predict either learning or transfer
What was the main effect for time in GA in Experiment 1? What was the main effect for accuracy? Please deliver results by independent variable.
IV: Question Type [Verbal vs. Arithmetic]
No difference for time in GA or accuracy
IV: Difficulty Level [Easy vs. Moderately Difficult]
More GA w/ moderately difficult items & more correct answers for easy questions
IV: GA Instruction [Treatment vs. Control]
More GA and higher rate of accuracy in Treatment group
What are significant differences that exist between how High Achieving Countries approach "Making Concepts" problems versus countries like Australia and the United States?
BONUS: What are some ways HACs approached problems like "Using procedures" that differed from countries like the US and Australia?
HACs that present a problem as a "making connections" problem tend to follow through with instructing the students in this manner. Meanwhile, the US and Australia will present a problem as a higher-level "making connections" problem and then mostly end up giving the answers outright, turning it into a procedural question, or turning it into a stating concepts questions.
BONUS: Teachers in countries like Hong Kong that initially present a problem as a "Using Procedures" question will end up working through it in a way that it challenges the students to do higher level thinking like "Making Connections".
What did the authors find in the Professor Quality study regarding "contemporaneous performance" and performance in subsequent courses?
BONUS: What metrics did the authors of the study use to determine "professor quality"?
The authors found an inverse relationship between contemporaneous performance and performance in subsequent courses. Students of professors of "higher quality" received lower grades than students of professors of "lower quality" - however, they performed better on more advanced courses than students who had "lower quality" professors.
BONUS: The authors used characteristics like academic rank, teaching experience, and terminal degree status to determine quality.
BONUS BONUS: The authors found that there was a negative correlation between these characteristics and performance on contemporaneous courses.
What impact did the expressive writing intervention have on students found to have high test anxiety? What about on students found to have low test anxiety?
BONUS: How did the researchers come to the conclusion that writing about negative thoughts and worries led to enhanced performance?
Hint: Recall what you can about Lab #2
The EW intervention was found to be most beneficial to students with high test anxiety. Students with low test anxiety didn't really experience any drawbacks or benefits from being in the EW intervention.
BONUS: They conducted an analysis of negative words and anxiety related words used in the students' writings. They found that the more anxiety related words used, the higher the post-test performance. This established that writing about anxiety was the mediating factor.
What is the relationship between uncertainty, curiosity, and transfer?
While uncertainty increased transfer [UU = EU > NU] and uncertainty increased curiosity [UU > EU > NU], condition was found to be what predicted a significant amount of variance in transfer scores as they relate to curiosity.
Correlation is NOT causation - just because curiosity tends to go up with transfer because both increase with uncertainty DOESN'T mean that curiosity CAUSES transfer and vice versa.
In summary - curiosity wasn't found to be a significant mediating variable between uncertainty and transfer.
Potential Short Answer Question: You're a teacher at an underfunded public school. The district is pressing you and your fellow teachers to boost exam scores to secure more funding. What strategies could you and your colleagues implement that are quick, immediate, and cost-effective?
1) Increase wait time(s)
2) For younger students, begin instructing them on Gaze Aversion
3) Provide students with opportunity to write about test anxieties they may have before an exam
and more...!
What are the distinguishing features of High Achieving Countries? How should countries like America use information like what's presented in TIMMS?
Distinguishing features of HACs include:
1) Besides the Czech Republic, HACs tend to spend more time introducing and working through new content. In contrast, US & AUS tend to spend a lot of time reviewing old content.
2) HACs tend to follow through on higher level type questions like "Making Connections" whereas countries like the US would take these amazing questions and undermine what makes them so beneficial for learning.
- Something to keep in mind is that teaching is a SYSTEM. There is no mechanism that currently exists in the US that would allow for massive changes in teaching and pedagogy.
- Nonetheless, the US can learn a lot. Incorporating the teaching practices that've found success in other countries into the training American teachers undergo would go a long way in rectifying the deeply ingrained ineffective practices prevalent in the nation.
Construct the full relationship between student evaluations, contemporaneous scores, professor quality, and performance in advanced courses. Explain the significance of this study as it pertains to current practices in higher education.
BONUS: What are possible reasons provided by the authors of the study as to WHY these results occur?
Student evaluations directly correlate with contemporaneous scores and are inversely correlated with: professor quality, performance in advanced courses, and deep learning.
Student evaluations don't appear to reward deeper learning or professor quality. This is deeply problematic as the current practice in higher education is to use student evaluations in a number of ways, including rewarding professors with tenure. The accuracy and ability of student evaluations to serve as an objective measure is seriously called into question by this study.
BONUS: The authors proposed that the reason contemporaneous scores may be higher when classes are taught by "lower-quality professors" is that they may tend to teach to the test or don't consider enough what students will need to learn in subsequent courses.
What was the relationship between: female teacher's math anxiety - girls' math achievement - girls' gender ability beliefs?
BONUS: What was the relationship between female teacher's math anxiety - boys' math achievement - boys' gender ability beliefs?
As female teacher math anxiety went up, so did girls' endorsement of traditional gender stereotypes. There was an inverse correlation between FT math anxiety and girls' math achievement - the more anxious the teacher, the lower the girls' scores.
BONUS: No impact at all was really observed in boys.