Walk into an early elementary school classroom and you are likely to see lots of manipulatives. From Popsicle sticks to Cuisenaire rods we have a strong intuitive sense that these objects should help children learn mathematics.
Not so fast, says Sara Fulmer over at The Learning Scientist;
Although manipulatives can increase students’ attention, this attention may not benefit their learning. In fact, the very aspect of manipulatives that capture students’ attention—bright colors, visual appeal, realistic features—may be their downfall. Manipulatives that are more visually interesting or realistic can increase off-task behavior, such as building or sorting (1). This is especially true if students interact with that object in other contexts, such as during play time or outside of the classroom.
Students who learn with manipulatives can become too reliant on the object and context, and as a result, have difficulty transferring their knowledge to new contexts, different testing formats, or to abstract representations (e.g., algebraic expressions) of the problem
A paper in the most recent issue of Learning and Individual Differences reports an interaction between an individual’s chronotype (the extend to which you are a morning or an evening person) and the timing of academic activities.
I think this is a potentially important result. It suggests that knowledge of a biologically mediated individual difference might allow us to optimize instruction for different students. From the abstract:
Results indicate a synchrony effect (interaction of time of day and chronotype) in achievement and state motivation. Evening types have worse achievement, lower interest, and lower joy in the morning, but there were no significant associations between chronotype and the outcomes in the afternoon. Since adolescent evening types can learn better and are more motivated in the afternoon, schools should offer more learning opportunities in the afternoon.
Here’s a paper, just published in Personality and Individual Differences, that explores students’ concepts of the ideal professor.
From the abstract:
Despite intuitions that the ideal teacher has a particular set of non-cognitive characteristics, there is little research investigating such issues. The current two studies investigate students’ descriptions of “ideal” instructor personality using the Five-Factor Model of personality. Both absolute personality preferences (certain traits are universally desired) and relative personality preferences (certain traits are desired relative to students’ own level of the trait) are examined among 137 first year mathematics students (Study 1) and 378 first year psychology students (Study 2). Students provided Big Five personality ratings for themselves, their actual instructor, and their ideal instructor. Supporting the absolute preference hypothesis, students rated their ideal instructor as having significantly higher levels than both themselves and the general population on all five personality domains (except for openness in Study 1), with particularly large effect sizes for emotional stability and conscientiousness. Supporting the relative preference hypothesis, students also rated their ideal instructor as having a similar Big Five profile to themselves.
As someone who teaches at the university level I found this quite interesting. In Piaget’s theory of development, teenagers and adults are in the formal operations stage. Piaget describes a kind of formal operations ego-centrism, where the individual compares abstract notions of perfection with reality and finds reality wanting. For example, adolescents will construct a notion of what perfect parents would be like, and then compare their real parents with the abstraction. Any guesses on how the real parents come out in this comparison?
So it seems that our students have ideas about the perfect instructor and we actual teachers suffer by comparison.
Does having an instructor who matches your ideal help your performance? Here is what this study found:
if their actual instructor’s personality was similar to their ideal instructor’s personality, students showed greater educational satisfaction (but not higher performance self-efficacy nor academic achievement).
I have blogged a number of times about the crisis in psychological research. Many widely publicized research findings have been called into question because of faulty methodology. These faulty methods include small underpowered studies, p-hacking, and failure to replicate.
Now the stereotype threat, the claim that awareness of a stereotype about one’s own group will lead to a reduction in performance, has been called into question.
“Stereotype threat is one of the most famous and influential ideas in psychology. It is thought to be a key explanation for group differences in performance – whether the group is defined by gender, race or class. But now, stereotype threat itself is under threat. New studies are questioning just how robust it is, and even whether it exists at all. The same goes for many other staples of social psychology – to the point where the whole edifice is tottering badly.”
Arizona has passed a law requiring high school pass the U.S. Immigration and Naturalization civics test for graduation. Let me state, that I have no firm position on if this is a good idea. However, I can recognize a bad argument against it.
This is the argument made by Joseph Kahne in Education Week, that schools should be teaching critical thinking instead of knowledge:
“Democracy thrives when citizens think critically and deeply about civic and political issues, when they consider the needs and priorities of others, and when they engage in informed action—not when they memorize a few facts. Let’s make high-quality civic learning a priority. Let’s not take the easy way out and pass laws in more than a dozen states that turn civic education into a game of Trivial Pursuit.”
The problem with this argument is that it is contrary to the evidence. Research on critical thinking and other higher order skills shows that deep knowledge is a necessary prerequisite.
I agree that a curriculum that only focuses on the memorization of facts is impoverished. But a curriculum that tries to teach higher order skills without the requisite knowledge is impossible.
You can take a sample citizenship test here. The questions are pretty easy and really do seem like things a citizen should know.
For more details on the importance of memory in education see the second chapter of my book.
Kevin Donnelly makes the case:
“Based on this recent study of classrooms in the UK and China and a recent UK report titled What makes great teaching?, there is increasing evidence that these new-age education techniques, where teachers facilitate instead of teach and praise students on the basis that all must be winners, in open classrooms where what children learn is based on their immediate interests, lead to under-performance.”
The original report can be found here. These are the key findings:
‘The two factors with the strongest evidence of improving pupil attainment are:
teachers’ content knowledge, including their ability to understand how students think about a subject and identify common misconceptions
quality of instruction, which includes using strategies like effective questioning and the use of assessment
Specific practices which have good evidence of improving attainment include:
challenging students to identify the reason why an activity is taking place in the lesson
asking a large number of questions and checking the responses of all students
spacing-out study or practice on a given topic, with gaps in between for forgetting
making students take tests or generate answers, even before they have been taught the material
Common practices which are not supported by evidence include:
using praise lavishly
allowing learners to discover key ideas by themselves
grouping students by ability
presenting information to students based on their “preferred learning style”’