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Growth Mindset and the CCSS Standards for Mathematical Practice go Hand-in-Hand

Posted by Cindy Bryant

Nov 16, 2013 2:30:00 PM

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For many years, intelligence was thought to be static (fixed) and could not be altered and informal research has shown this to be particularly true when it comes to students thinking about their mathematics intelligence. But with the advent of advanced technology and cognitive labs, top cognitive psychologists and neuroscientists have found that aspects of intelligence and even intelligence itself can be altered through training and experiences.

Exposing individuals to new learning experiences serves as a way of working or exercising the brain and we know that exercising makes something stronger, so it makes sense that exercising the brain makes it stronger. The brain becomes stronger when we learn something new and unfamiliar by creating new connections that can be stored in memory that provide frameworks to link new knowledge by association. In other words, “What we already know determines to a great extent what we will pay attention to, perceive, learn, remember, and forget” (Woolfolk, 1998. p.227).[i]

Brain scientists define learning as a process that will modify a subsequent behavior and memory is the record left by a learning process, but they are dependent on each other as illustrated below.

GrowthMindset_Image2

But it it’s more than just providing a new learning experience. The work of Carol Dweck of Stanford University bridges developmental psychology and social psychology, and examines the self-conceptions (or mindsets) that we use to structure the self and guide behavior. In her research regarding student motivation, she has studied the origins of mindsets, their role in motivation and self-regulation, and their impact on achievement and interpersonal processes.

Some of Dweck’s (Mindset, 2006)[ii] work includes research with 373 seventh grade students with equal prior math achievement to determine how a fixed mindset (the belief that intellectual abilities are fixed) compared to growth mindset (the belief that intelligence can be developed) impacted math achievement. In her eight-week intervention program, some of the students were taught study skills and growth mindset or how they could learn to be smart because their brain was a muscle that becomes stronger the more it’s used. The control group learned the study skills but not the growth mindset or expandable theory of intelligence. The results of the study showed the treatment group or growth mindset students, who embraced the belief that intellectual abilities can be cultivated and developed through application and instruction had marked improvement in grades and study habits in comparison to the control group. By the end of the fall term, the math grades had jumped apart and continued to diverge over the next two years.

Additionally, Dweck (Mueller & Dweck, 1998) has studied the relevance of the types of praise that teachers offer students in conveying mindset. Her study with 5th grade students shows that when teachers used person praise (for their intelligence) it tends to put students in a fixed mindset whereas when using process praise (for their effort/procedure) it tends to foster a growth mindset.

Dweck’s mindset theory goes hand-in-hand with the Standards for Mathematical Practice (SMPs)[iii] in conveying a growth mindset in the classroom. The key element between a fixed mindset teacher and a growth mindset teacher is in how they view struggling students. The fixed mindset teacher perceives students that struggle as not sufficiently bright, talented or smart in the subject whereas the growth mindset teacher sees struggling students as a challenge - as learners who need guidance and feedback on how to improve. Growth mindset teachers view efforts and mistakes as highly valued and can be used as an opportunity for students to learn.

First and foremost, the SMPs stress the relevance and importance of persevering in solving a problem and learning from mistakes both of which echo the growth mindset of valuing and learning from mistakes. Additionally, the SMPs focus on using multiple processes and procedures for solving problems and students being able to share their various ways of solving problems. As Dweck found, process praise for the effort or procedure was powerful in developing growth mindset, so it’s important for students to have opportunities to learn and use different processes and procedures in solving problems and for teachers to praise the process and not the person.

Ultimately, the SMPs provide ample opportunities for making connections and exercising the brain. In offering a variety of instructional strategies and activities, growth mindset teachers maximize opportunities for multiple interactions with mathematics. A classroom steeped in the SMPs allows students to actively discover, interpret, analyze, process, practice, and communicate - all of which have the potential to move information from working memory into long term memory and ultimately expanding brain power and mathematics intelligence.  

Growth mindset, the belief that intellectual abilities can be cultivated and developed through application and instruction, and the SMPs go hand-in-hand in helping students become successful math students. But more importantly, they are critical in helping students become life-long learners and problem solvers.[

For many years, intelligence was thought to be static (fixed) and could not be altered and informal research has shown this to be particularly true when it comes to students thinking about their mathematics intelligence. But with the advent of advanced technology and cognitive labs, top cognitive psychologists and neuroscientists have found that aspects of intelligence and even intelligence itself can be altered through training and experiences.

Exposing individuals to new learning experiences serves as a way of working or exercising the brain and we know that exercising makes something stronger, so it makes sense that exercising the brain makes it stronger. The brain becomes stronger when we learn something new and unfamiliar by creating new connections that can be stored in memory that provide frameworks to link new knowledge by association. In other words, “What we already know determines to a great extent what we will pay attention to, perceive, learn, remember, and forget” (Woolfolk, 1998. p.227).[i]

Brain scientists define learning as a process that will modify a subsequent behavior and memory is the record left by a learning process, but they are dependent on each other as illustrated below.

But it it’s more than just providing a new learning experience. The work of Carol Dweck of Stanford University bridges developmental psychology and social psychology, and examines the self-conceptions (or mindsets) that we use to structure the self and guide behavior. In her research regarding student motivation, she has studied the origins of mindsets, their role in motivation and self-regulation, and their impact on achievement and interpersonal processes.

Some of Dweck’s (Mindset, 2006)[ii] work includes research with 373 seventh grade students with equal prior math achievement to determine how a fixed mindset (the belief that intellectual abilities are fixed) compared to growth mindset (the belief that intelligence can be developed) impacted math achievement. In her eight-week intervention program, some of the students were taught study skills and growth mindset or how they could learn to be smart because their brain was a muscle that becomes stronger the more it’s used. The control group learned the study skills but not the growth mindset or expandable theory of intelligence. The results of the study showed the treatment group or growth mindset students, who embraced the belief that intellectual abilities can be cultivated and developed through application and instruction had marked improvement in grades and study habits in comparison to the control group. By the end of the fall term, the math grades had jumped apart and continued to diverge over the next two years.

Additionally, Dweck (Mueller & Dweck, 1998) has studied the relevance of the types of praise that teachers offer students in conveying mindset. Her study with 5th grade students shows that when teachers used person praise (for their intelligence) it tends to put students in a fixed mindset whereas when using process praise (for their effort/procedure) it tends to foster a growth mindset.

Dweck’s mindset theory goes hand-in-hand with the Standards for Mathematical Practice (SMPs)[iii] in conveying a growth mindset in the classroom. The key element between a fixed mindset teacher and a growth mindset teacher is in how they view struggling students. The fixed mindset teacher perceives students that struggle as not sufficiently bright, talented or smart in the subject whereas the growth mindset teacher sees struggling students as a challenge - as learners who need guidance and feedback on how to improve. Growth mindset teachers view efforts and mistakes as highly valued and can be used as an opportunity for students to learn.

First and foremost, the SMPs stress the relevance and importance of persevering in solving a problem and learning from mistakes both of which echo the growth mindset of valuing and learning from mistakes. Additionally, the SMPs focus on using multiple processes and procedures for solving problems and students being able to share their various ways of solving problems. As Dweck found, process praise for the effort or procedure was powerful in developing growth mindset, so it’s important for students to have opportunities to learn and use different processes and procedures in solving problems and for teachers to praise the process and not the person.

Ultimately, the SMPs provide ample opportunities for making connections and exercising the brain. In offering a variety of instructional strategies and activities, growth mindset teachers maximize opportunities for multiple interactions with mathematics. A classroom steeped in the SMPs allows students to actively discover, interpret, analyze, process, practice, and communicate - all of which have the potential to move information from working memory into long term memory and ultimately expanding brain power and mathematics intelligence.  

Growth mindset, the belief that intellectual abilities can be cultivated and developed through application and instruction, and the SMPs go hand-in-hand in helping students become successful math students. But more importantly, they are critical in helping students become life-long learners and problem solvers.

[i] Woolfolk, A. (1998). Educational Psychology (7th ed.). Needham Heights, MA: Allyn & Bacon

[ii] http://mindsetonline.com/thebook/buythebook/index.html

[iii] http://www.corestandards.org/Math

Topics: Differentiating Instruction, Implementing the Common Core, Resources, Teaching & Learning

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