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Literature Reviews:

Literature Reviews:

Author: Tammy Long

In the beginning stages of research and all throughout the process, rather than completely reinvent the wheel, I culled through what other researchers have discovered about how a student’s attitudes affected their performance in the classroom.  From my years of classroom experience, I had an idea of what I thought were solutions to math anxieties and stereotyping.  My initial literature research stemmed from those instinctual notions but as I began collecting more attentive data than casual observations, I fine-tuned and expanded my printed resources.  My hope was to let my findings lead me to more focused research and deeper understanding of how to give math students the best education so that it will be a positive impact on their lifelong learning.

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Learning Environment

When a student enters a classroom for the first time, the environment is what they evaluate first.  Is the furniture arranged to be inviting or stiff and cold?  Are the walls bare, covered in static information, or inviting?  Does the teacher seem to care the student has arrived?  These and many more factors set the tone for learning.  Stress, ramped up or minimized, can determine whether a child can even begin to learn new material. 

“Neuroscientists have discovered that learning takes place as three parts of the brain interact: the amygdala, which responds to emotion; the hippocampus, which moves experiences to long-term memory; and the cerebral cortex, where information is stored.  In the ideal learning experience the student feels confident and engaged. The pleasant atmosphere and novelty of the material releases the amygdala and allow the hippocampus to begin transmitting the new information to the cerebral cortex.  In a stressful situation, however, brain function radically changes the amygdala becomes over-stimulated and blocks access to the hippocampus; in addition, cortisol (a hormone released when a person is under stress) attaches itself to the hippocampus, preventing it from functioning.  Thus, the information can’t get to the cerebral cortex for long-term storage.”  (Demme, 2015)

Classroom discipline makes up a significant part of the learning environment.  All veteran teachers know, if the class is out of control, it’s difficult for anything to get done.  Having a well-structured and peaceful classroom does not have to include punishment and emotional manipulation.  Child psychologists have long known the damaging effect of punishment, rewards, and praise.  The simple expressions, “Good boy/girl,” and, “I’m proud of you,” have set up a dynamic where the child now feels they must work to live up to the standards of someone else.  Their internal voice is stifled as they are trained to seek external validation.  Changing that dialog into validating statements like, “You worked hard on that,” and, “You’re proud of yourself,” encourages the student, acknowledges the student’s effort, and keeps their motivation internal.  Teaching a child to self-validate teaches them to self-modulate.  Behavior charts and punishment may get immediate results, but they will be short term and as the system gets challenges, the stakes must be raised.  Allowing students choices and natural consequences fosters a positive student-teacher relationship built on respect.   Title I teacher, Nikki Sabiston, offers a personal story about her child and the adverse outcome of behavior charts and some alternatives in the classroom based on the Responsive Classroom model.  “My school uses a ‘Take a Break” space…..not a traditional ‘Time Out’…..where children can take a moment to decompress, take a breather, or think about making different choices.  The students often go there on their own…” (Sabiston, 2012)

Valerie Strauss from the Washington Post offers the following weaknesses in many educational systems.  Her article, “Ten Obvious Truths About Educating Kids That Keep Getting Ignored” gives more detail about each bulleted item.

1.      Much of the material students are required to memorize is soon forgotten.

2.      Just knowing a lot of facts doesn’t mean you’re smart.

3.      Students are more likely to learn what they find interesting.

4.      Students are less interested in whatever they’re forced to do and more enthusiastic when they have some say.

5.      Just because doing x raises standardized test scores doesn’t mean x should be done.

6.      Students are more likely to succeed I a place where they feel known and cared about.

7.      We want children to develop in many ways, not just academically.

8.      Just because a lesson (or book, or class, or test) is harder doesn’t mean it’s better.

9.      Kids aren’t just short adults.

10.  Substance matters more than labels.

As these concerns are expressed, we as educators should listen and do what we can to address them.  Making tweaks in how the classroom is governed is a huge first step.

Curriculum and Instruction

Multiple studies have shown that a positive learning environment leads the way for optimal scholarship.  Much debate happens around the type of curriculum and method of delivery.  Fostering a safe setting for students to try and fail is not just part of their learning environment, it is also how lessons are designed and presented.  Teaching about how to learn and how to handle obstacles and failure have as much impact as the core subject matter for a student.  From a constructivist perspective, mistakes are desirable.  By appreciating mistakes, one can overcome the fear of trying and empower themselves to take risks.  Knowing the stakes of such risk of failure is just as important.  Eduardo Briceno organizes four types of mistakes according to learning opportunity and intentionality.

Stretch mistakes have the highest reward.  These happen when we are purposefully trying to acquire a new skill and do something incorrectly.  We are stretching beyond what we already can do.  Stretch mistakes mean we are challenging ourselves.  Aha- moments are also positive, but happen when we realize we can fine tune our methods.  Maybe the rule of four always works for finding a common denominator when adding fractions; but for some cases, there are shorter methods.  These breakthroughs often happen while reflecting on an accomplishment.  Sloppy mistakes have learning value, as we are all human and make them.  When we’re doing something we’ve already mastered and lose concentration, we can make sloppy mistakes.  When tired or unfocused, many students want to divide by two when finding the square root even though they’ve shown mastery countless times before.  High-stakes mistakes include choices with devastating consequences like driving too fast or distracted.  Less threatening situations that are more typical of a classroom would be not preparing for a final or entrance exam.  Performances and speeches can be considered high-stakes by most people.  Failing in these areas will impact our lives deeper and longer than not simplifying your final answer.  While learning from our mistakes requires reflection and effort, the energy is well spent. 

“If we’re more precise I our own understanding of mistakes and in our communication with students, it will increase their understanding buy-in, and efficacy as learners.” (Briceno, 20150

Just as teaching the value of correcting mistakes is vital to learning, how an educational system is organized can foster more growth or more stress depending on the style.  Deviating from classifying students by age and grade level has shown encouraging results.  Campuses that focus on ability level over grade level free up the students to focus on the path of learning rather than checking to see if they measure up to their peers in the same grade and/ or age range.  Instead of slotting a child in a developmental math class or require extra tutorials, some institutions have math classes according to levels that you work through at your pace.  This eliminates stereotyping of both retarded and nerdy natures.  The students simple get to be themselves and feel valued.  Boxing in students’ potential fills their minds with “interfering thoughts, it makes effort disagreeable, and it leads to inferior learning strategies.  What’s more, it makes other people into judges instead of allies.”  (Dweck, 2006).   Regardless of how engaging the lesson is or how revolutionary the curriculum is, if a student’s ability doesn’t match the level of the instruction, little learning will happen.  True differentiated learning becomes possible when ability levels replace grade levels.

Taking the idea of teaching ability levels over grade levels to another level, some families are discovering the benefit of letting the child control their own learning.  Math is a skill that has evolved from real life situations.  Math describes life.  It predicts it.  It resolves problems and explains processes.  It is life and is all around us.  Allowing students to interact with the world around them will organically expose them to learning even something as specific as mathematics. “The best evidence I know that math is not hard comes from the experiences of people involved in the unschooling movement and the Sudbury “nonschool" school movement….where kids of all ages are free all day to interact with whomever they choose and pursue their own interests….All available evidence show that the kids in these setting grow up to become happy, productive, ethical members of the larger society, who continue to take charge of their own lives and learning throughout adulthood..” (Gray, 2010) The common thread of the various approaches to curriculum and instruction seem to be either a focus on what the program can provide to foster a lifelong learner or on scoring well on a standardized test.  Research is mounting about the ways we are teaching this generation.  With so much at stake, we owe it to them to cull through and find the best options for them.


Both my internal voice and my recent more formal research have shown me that while curriculum, instruction style, and learning environment set the tone in which a student may learn optimally; it is mindset that seems to determine whether a student will be successful in a challenging situation like learning advanced math concepts.

“…our studies show that teaching people to have a ‘growth mind-set,’ which encourages a focus on effort rather than on intelligence or talent, helps make them into high achievers in school and in life.”  (Dweck, 2006)

The New York Times recognized math anxiety as serious problem and suggested it was an attitude passed down from a child’s guardian.  In the article, “Square Root of Kids’ Math Anxiety: Their Parents’ Help.” Hoffman reveals research that children helped by math-anxious parents learned less math overall, fell behind their peers, and were more likely to develop math anxiety themselves.  As parents and educators, being stand in parental influences at school, we want to remove obstacles from our children’s journey through acquiring new knowledge, not create them.

Math bias may begin in the home environment, but has become a cultural stereotype.  In the article, “’Not a Math Person’: How to Remove Obstacles to Learning Math,” Schwartz describes the research done by Stanford math professor Jo Boaler over how this is affecting the current generation’s ability to learn math.  “We live in a society with lots of kids who don’t believe they are good at math.” (Schwartz, 2015)  Boaler offers the neuroscience to prove how what we think we can and cannot do becomes a self-fulfilling prophecy.   This false belief that a math brain gives people the innate ability to do math or not has created a fixed mindset.  Fostering a growth mindset in the mathematics classroom begins with the structure of classrooms.   Students should not be labeled and collated per abilities like “advanced” or “remedial.”  Mixed ability groups with “low-floor/high-ceiling” tasks allow all the students to participate as well as foster growth in their thinking process.  Boaler offers classes in person and online to help an educator make more changes in the instruction and learning environment to address the underlining goal; to convince people they can indeed do math, even elementary teacher.  Mindset as applied to mathematics becomes paramount when addressing that, “Many find math to be the most difficult and hated subject in school.” (Schwart, 2015)

 One of the forerunners in mindset research is Carol Dweck.  In her book, “Mindset: The New Psychology of Success,” she explains why people differ in how they utilize their assets and limitations.  Why do some highly “intelligent” people fail?  Why do others with what should be crippling learning “disabilities” triumph?  Dweck’s research shows people with what she calls a growth mindset achieve more and experience more success in spite of obstacles.  When a student’s grades fall and their explanations include defensive responses like, “I suck at math,” or, “The math teacher ....[assign some kind of blame to deflect from the believe they do not possess the ability to do the required task],”  they are trapped in a fixed mindset.  The student with a growth mindset sees a low grade as feedback on what they need to work on some more.  It’s an opportunity to rise to the challenge of figuring out the puzzle.  Their self-worth is not at stake.  When they believe they can get smarter, that learning is the goal, and that effort makes you stronger, they want to spend more time trying, work harder, and ultimately achieve more than those stuck in a math rut.