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Carol Dweck's work on mindsets has proven both popular and influential across schools over the last decade. The general thrust of her work is students with a growth mindset believe that their intelligence is not fixed, embrace mistakes as learning opportunities, and strive to improve through practice. This can be most readily seen in her book, Mindset. Whilst I see the advantage of having a growth mindset, I am yet to be fully convinced of how to practically develop such a way of thinking in my students. I share some more thoughts in my Takeaways below. 

Research Paper Title:
Boosting Achievement with Messages that Motivate
Author(s): Carol S. Dweck
My Takeaway:
A great introduction to Dweck's work on Mindset. She outlines her belief that students with a fixed mindset follow the cardinal rule "look smart at all costs", which leads to their desire to not work hard, not make mistakes, and if you do make mistakes to not try to repair them. In contrast, those with a growth mindset follow the rule "it is much more important to learn than get good grades", which leads them to take on challenges, work hard, and correct any mistakes. Studies quoted show that teaching students a growth mindset results in increased motivation, better grades, and higher achievement test scores
My favourite quote:
Many teachers see evidence for a fixed mindset every year. The students who start out at the top of their class end up at the top, and the students who start out at the bottom end up there. Research by Falko Rheinberg shows that when teachers believe in fixed intelligence, this is exactly what happens. It is a self-fulfilling prophecy. However, when teachers hold a growth mindset, many students who start out lower in the class blossom during the year and join the higher achievers.

Research Paper Title: Is it true that some people just can't do math?
Author(s): Daniel J Willingham
My Takeaway:
This is a really sensible discussion, backed by research, into the effect of student's ability and mindset when it comes to high school mathematics. Willingham argues that whilst it is true that some people are better at maths than  others - just like some are better than others at writing or building cabinets or anything else it - is also true that the vast majority of people are fully capable of learning the levels of mathematics they need for high school. We have seen in the Cognitive Science section that learning mathematics is Biologically Secondary knowledge, and so does not come as naturally as learning to speak, but our brains do have the necessary equipment. So, learning maths is somewhat like learning to read: we can do it, but it takes time and effort, and requires mastering increasingly complex skills and content. I love this bit: "Just about everyone will get to the point where they can read a serious newspaper, and just about everyone will get to the point where they can do high school level algebra and geometry even if not everyone wants to reach the point of comprehending James  Joyce's Ulysses or solving partial differential equations." For Willingham, in order to be successful in maths, students need the following three types of knowledge:
1) Factual - this is knowledge of times tables and number bonds which must be automated as discussed in the Fluency section. As we have seen throughout the research studies on this page, without this knowledge students' working memories are likely to become overloaded when attempting to solve more complex problems.
2) Procedural - this is a sequence of steps by which a frequently encountered problem may be solved. This may involve using the gird method for long multiplication, or SOHCAHTOA for trigonometry questions.
3) Conceptual - this refers to an understanding of meaning; knowing that multiplying two negative numbers yields a positive result is not the same thing as understanding why it is true.
These latter two types of knowledge form the basis for the conflicts between progressives and traditionalist views of maths education. Conceptual knowledge is probably the most difficult type for students to acquire, but it is of fundamental importance as new mathematical concepts almost always build on previous ones (for example, a clear understanding of the equals sign is needed to solve linear equations). Without this conceptual knowledge, students are forced to rely on algorithms to carry out procedures, but given the amount of procedures in mathematics, not to mention to difficulty of spotting which procedure is required, means this is simply unsustainable. What does all of this mean for maths teaching, and for the issue of mindset, I hear you ask? Well, Willingham has five pieces of advice for maths teachers, each of which is expanded upon in the paper:
1) Think carefully about how to cultivate conceptual knowledge, and find an analogy that can be used across topics
2) In cultivating greater conceptual knowledge, don't sacrifice procedural or factual knowledge
3) In teaching procedural and factual knowledge, ensure that students get to automaticity
4) Choose a curriculum that supports conceptual knowledge
5) Don't let it pass when a student says "I am no good at maths"
And it is the final point that brings us back to mindset. For Willingham, as the quote below illustrates, maths is something that can be learned through hard work and good teaching. As I said in my introduction, I firmly believe the concept of a growth mindset is important, but we need to help the students see that their achievement in maths can be changed for the better.
My favourite quote:
We hear it a lot, but it's very seldom true. It may be true that the  student finds math more difficult than other subjects, but with some persistence and hard work, the student can learn math and as he learns more, it will get easier. By attributing the difficulty to an unchanging quality within himself, the student is saying that he's powerless to succeed.

Research Paper Title:
Academic Tenacity: Mindsets and Skills that Promote Long-Term Learning
Author(s): Carol S. Dweck, Gregory M. Walton, Geoffrey L. Cohen
My Takeaway:
This particular paper presents some compelling findings and practical strategies to help foster a growth mindset and develop academic tenacity. Two findings that stood out to me were:
1) Students who received effort praise chose challenging tasks that could help them learn, while students who received intelligence praise were more likely to choose tasks in their comfort zone that they could perform well on;
2) Classrooms that encourage competition and individualistic goals may be particularly ill suited to minority students, who are more likely to be reared in cultural contexts that emphasize the importance of communal and cooperative goals over individualistic or competitive goals.
My favourite quote:
Research shows that students’ belief in their ability to learn and perform well in school—their self-efficacy—can predict their level of academic performance above and beyond their measured level of ability and prior performance

Research Paper Title:
Does mindset affect children’s ability, school achievement, or response to challenge? Three failures to replicate.
Author(s): Yue Li & Timothy C. Bates
My Takeaway:
I include this paper for balance as it was the most empirically rigorous one I could find that questions Dweck's findings on mindset. Specifically, the authors find praise for intelligence failed to harm cognitive performance and children’s mindsets had no relationship to their IQ or school grades. Finally, believing ability to be malleable was not linked to improvement of grades across the year. Two points I would raise here: the authors do not find that promoting mindset beliefs to have a negative effect, and more importantly work by the likes of Dan Willingham and others discussed above strongly believe that effort and practice can significantly increase achievement. Hence, I personally have no problem promoting a growth mindset, both in students and teachers. However, a growth mindset without the success that will most likely follow from an Explicit Instruction approach may not be sustainable in the long run, in my opinion.
My favourite quote:
We find no support for the idea that fixed beliefs about basic ability are harmful, or that implicit theories of intelligence play any significant role in development of cognitive ability, response to challenge, or educational attainment.