Background
What is a Learning Disability?
Within the classroom, learning disabilities are characterized by a significant difference between a child's achievement and that individual's overall intelligence. Initially, the regular education teacher who has observed a difference in student ability compared to their grade level peers identifies students. Students are then referred to a special education teacher to complete formal cognitive reading and/or math assessments. If a deficit, for example, is identified meaning students score is below their actual grade level, students are referred (with parental consent) to the school psychologist to complete additional testing. Students found to have a learning disability are normally two grade levels below their age appropriate peers.
Scientific research defines a learning disability as a neurological disorder that affects the brain's ability to receive, process, store, and respond to information. These disabilities can make it difficult to acquire certain academic and social skills . 6 "Learning disorders affect about two million children between the ages of six and seventeen, or about one out of every twenty school children. These children have problems learning new information, remembering that information, and knowing how to transfer the information for practical purposes. The three main types of learning disorders are reading, mathematics, and writing." 7
Anatomy and Function of the Brain
A recurring idea that is mentioned by neuroscientists is that the human brain is a complex and amazing structure. As a result, research in this area continues to expand, including as it relates to how the brain learns math. In the past, reading was given greater research effort, due to societal emphasis on reading comprehension. Nevertheless, over the past two decades, math brain research has made significant findings.
The brain is approximately three pounds and is divided into three main parts. They are known as the cerebrum, cerebellum, and the brain stem. Each part serves a different function. The cerebrum made of two distinct hemispheres makes decisions that require conscious thought, sensation, and voluntary movement. The cerebellum controls balance and coordination. The brain stem involves involuntary actions such as breathing and heartbeat. However, for this unit, the focal point is on the four major lobes and the limbic area.
The cerebral cortex or the exterior part of the brain is divided into four sections known as lobes: frontal, temporal, occipital, and parietal lobe. The frontal lobe is important for planning and thinking. Most of working memory is located in the frontal lobe. Broca's area in the left frontal lobe processes our language vocabulary, including number words.
David Sousa mentions that the frontal lobe matures slowly and usually it is not fully developed until the age of 24. This information helps to explain why adolescents engage in impulsive emotional responses. The temporal lobe is responsible for sound, music, face, object recognition, and some parts of long-term memory. The occipital lobe is almost exclusively for visual processing. The parietal lobe deals mainly with spatial orientation, calculation, and certain types of recognition.
Buried within the cerebrum is an interior part of the brain that is important for our math study: the limbic area. It consists of four sections that are essential for memory and learning. Section one the thalamus, which is responsible for all incoming sensor information, except for smell. Initially, sensory information travels to the thalamus and then goes to other parts of the brain for processing. Section two is the hypothalamus, which maintains the equilibrium within the body. This part of the brain impacts our students because if the hypothalamus is out of balance, then it becomes difficult for them to concentrate on academic processing. Section three is the hippocampus, which according to Sousa plays a major role in consolidating learning and in converting information from working memory via electrical signals to the long-term storage regions. The process may take days to months and is essential for the creation of meaning. Section four is the amygdala, which impacts emotions, particularly fear.
Learning and Memory
According to Sousa, "learning is the process by which we acquire knowledge; memory is the process by which we retain it." 8 This comment represents one of the fundamental purposes of my unit. I believe that my learners have the cognitive ability to learn new concepts and retain them. So, I will provide them with the tools and strategies to bring these ideas to fruition. My first step is to acknowledge that learning and retention occurs differently in individuals. When students learn they use the brain and the environment. The interaction of the two, facilitate learners to acquire information and skills. Conversely, retention requires the learner to do several things. During instruction, the student needs to maintain focus. Because students with learning disabilities often have some form of attention deficit disorder, it is difficult for them to remain focused for extended periods. Simultaneously, they need to build conceptual frameworks that have sense and meaning. Eventually, the goal is for student learning to consolidate into long-term memory.
Have you ever taught a new skill and students appear fully engaged? Then, to discover a week later, they do not remember basic information. Many students lack the capability to retrieve information, which Sousa defines as "rehearsal a critical component in the transference of information from working memory to long-term storage." 9 He mentions that the brain's decision to retain learning seems to be based on two criteria: sense and meaning. Does the student understand what they have learned and does the student gain a personal connection? Sousa further states that sense and meaning requires repetitive occurrences and time for authentic learning to occur.
Sousa expounds on two types of rehearsal: rote and elaborative. Rote rehearsal is used when learners need to remember and store information exactly into working memory. 1 0 It is a basic and commonly used strategy practiced by students with learning challenges. Elaborative rehearsal is used when it is unnecessary to store information exactly as learned, and when it is important to associate new learning with prior learning to detect relationships. 1 1 This is a complex thinking process that requires students to review the information, make connections to prior knowledge, and to make meaning. Rarely do special education learners implement elaborative rehearsal. For example, students would use rote rehearsal to memorize multiplication facts, but elaborative rehearsal to multiple fractions. Consequently, students with learning disabilities need more time and guidance than others to rehearse the new learning in order to determine sense and recognize meaning.
To improve my instructional practices and enhance student learning, a deliberate concentration on meaning is necessary. An eye-opening revelation is Sousa's comment that experimental and anecdotal evidence reveals that mathematical content does not have meaning for students. 1 2 Meaning becomes an essential element because if the content being taught has meaning and makes sense then retention occurs. Therefore, I want to maintain my current classroom environment where students are encouraged to reflect upon their learning and ask questions when they do not understand a concept. A simple statement "I do not get this" is an indicator that students have not made sense of the learning and/or they do not feel that the learning is relevant. We cannot deny the importance of meaning when brain scans show dramatically increased cerebral activity when new learning makes sense and is connected to prior experience, whereby improved retention follows. More often than not, without meaning students blindly memorize procedures without understanding how and why they work.
Previously neuroscientists believed that humans had two major memories: short-term and long-term memory. Current research has uncovered that we have two temporary memories and one long-term memory. Immediate memory stores information for seconds whereas working memory stores information from minutes to days. Long-term memory stores information for years. The two major types of long-term memory are declarative (conscious or explicit) and nondeclarative (implicit) memory. Declarative memory has two components: episodic involves autobiographical information; and semantic involves words, facts, objects, and faces. It is also important to mention that declarative memory improves when combined with elaborative rehearsal. Nondeclarative memory has three components, which are procedural (meaning rote motor and cognitive skills), conditioning, and nonassociative learning. Why is having accessibility to this information imperative for teachers? Because the more emphasis that teachers place on declarative processes involving understanding and meaning, the more likely children will succeed and actually enjoy math. A declarative-based approach encourages reflective inquiry and allows opportunities for students to become creative decision makers on how to solve problems.
Why Do Students Have Learning Disabilities?
Until recently, science could tell us little about the causes of learning disorders and even less about ways to address them successfully. Recent research and brain studies, including the development of imaging and other technologies, have enabled neuroscientists to look inside the live brain and gain new knowledge about its structure and functions. One type of research on learning disorders compares the functions of brains without deficits to the functions of brains with deficits. The latest research has shown that learning disabilities do not stem from a single cause but from difficulties in bringing together different regions of the brain. 1 3 Currently, the general consensus among researchers is that most genes associated with common learning disabilities, such as language impairment, reading problems, and mathematics, are not specific ones. As a result, no one strategy, technique, or intervention can address all student needs. Some additional factors that affect brain development are genetic links, tobacco, alcohol, and other drugs, problems during pregnancy or delivery, and toxins or stress in the child's environment.
Neil Sturomski mentions several reasons why students have learning disabilities. 1 4 First, students are overwhelmed, disorganized, and frustrated in new learning situations. Second, due to prior unsuccessful attempts, they have given up and developed low self-esteem and low expectations for achievement of the stated goals. Third, persistent apathy about learning happens because they have not made the connection to the importance of academic success. Unfortunately, I have observed these behaviors in my classroom.
Student inability to make the distinction between rote and elaborative rehearsal has severely impacted their achievement. Compound cognitive challenges with unrealistic school district's expectations that students' with math deficits are required to master new and multiple concepts based upon an aggressive pacing schedule. The result in the classroom, according to Sousa, is that students resort more frequently to rote rehearsal for nearly all processing. They are able to memorize facts but are unable to transfer the information to solve problems. "Consequently, they fail to make the association or discover the relationships that only elaborative rehearsal can provide." 1 5 Consistently they are unable to answer higher-order questions that require them to apply prior knowledge to new learning, especially when the problem has several solutions.
Nevertheless, Sousa's idea about future research makes me optimistic. "As we gain a greater understanding of the human brain, we may discover that some students designated as 'learning disabled' may be merely schooling disabled." 1 6 And as he suggests, "just changing our instructional approach may be enough to move students to the ranks of successful learners." 1 7 But, a more comprehensive approach to address disability challenges will require a collective effort among neuroscientists, psychologists, computer experts, parents, and teachers.
How Do We Learn Math?
Research in cognitive neuroscience has elaborated a timeline of how number structures develop in the brain of children from ages three through eleven. This research allows for some generalizations. Sharon Griffin and her colleagues learned that significant reorganization occurs around age five and that changes in cognitive structures occur every two years through the age of ten. 1 8 The findings indicate that sixty percent of children develop appropriately and twenty percent will develop below or above the norm.
A primary skill that is critical for students to attain is number sense. Russell Gersten and his colleagues define number sense as the ability to recognize that an object has been added or removed from a collection. 1 9 They go on to compare the early acquisition of number sense, understanding basic arithmetic, correlates to phonemic awareness, which is a prerequisite to learning phonics and becoming a successful reader. Usually, children whose number sense is not developed typically encounter future math challenges. "Number sense, then, can be considered the innate beginnings of mathematical intelligence." 2 0 Also, some evidence indicates that when a person is performing basic arithmetic, the greatest brain activity occurs in the left parietal lobe and in the region of the motor cortex that controls the fingers. 2 1 This may explain why younger children automatically use their fingers for counting. It is crucial to note the brain processes numerical symbols and number words in different locations. Sousa reveals, "the human brain comprehends numerals as quantities, not as words. This reflex action is deeply rooted in our brains and results in an immediate attribution of meaning to numbers." 2 2
The natural progression after mastering number sense is learning to calculate. Due to our genes, the human brain has serious problems with calculations. Part of the problem might be attributed to how the brain translates and tries to find mental representations for large numbers.
As a rule, multiplication is the next skill because students need to manipulate large numbers. Imaging studies show that the brain recruits more neural networks during multiplication than during subtraction. The difficulties could be due to associative memory, pattern recognition, and language. Thus, it makes sense that students with learning disabilities encounter challenges.
Learning for preadolescent ages six through twelve is heavily dependent upon maturity. Previously, it was believed that this age group had a learning pause, but new research shows they can solve more difficult problems, since the gray matter in the brain continues to increase. The gray matter in the brain is responsible for sensory perception, such as seeing and hearing, muscle control, speech, numerosity, and emotions. At puberty the brain is nearly at its full adult size. For that reason, by sixth grade these students have the ability to incorporate sophisticated math strategies. An area that matures later, and impacts student proficiency to use multiple approaches to problems, is the frontal lobe.
Adolescents, between the ages of thirteen through seventeen, are unique in their ability to successfully engage in answering additional complex and abstract problems. Scientists have discovered this new information about brain growth from imaging studies using Functional Magnetic Resonance Imaging (fMRIs), which is a major source of the study. Researchers found that adolescents used more of their prefrontal cortex than adults. As mentioned above, the prefrontal cortex, which is part of the frontal region of the brain, is not fully developed until approximately around the age of 24. Student concentration in this area has the potential to present trouble given that their response to problem solving can be emotional rather than rational. As the temporal lobes mature, adolescents improve in their visual and language processing skills. Another difficulty for adolescents is that their working memory matures slowly. Adolescents can have difficulty working with problems that have more variables and/or components than working memory's limited capacity can handle. Essentially, teachers need to remember that the adolescent brain is developing at various stages with a maximum of information that it can process at once. Therefore, teachers need to uncover diverse and meaningful applications of mathematical operations or concepts to maintain interest and attention.
Additionally, the way math is taught in schools is not directly correlated to how the brain processes numerical information. As students transition from elementary to the middle grades, the content is abstract and comprehension problems persist. Sousa mentions that children encounter a shift from primary grades when they move from an intuitive understanding of math to rote learning, as a result meaning is lost. 2 3 In summary, Sousa assertions that mathematical competence involves a blend of skills, knowledge, procedures, understanding, reasoning, and application makes sense and correlates to my actual classroom experience.
Student Environment Today Versus Yesterday
My conversations with colleagues suggest that children today learn differently from children from the 1960's, 1970's and even the 1980's. I found reading about today's student enlightening; it is one of the factors that has motivated me to include student-focused strategies in my unit. Hopefully, this brief comparative list will shed some light on the reason for these differences in how students learn.
Due to the advent of technology in almost every aspect of our daily life, teachers in the classroom encounter students who are technological and media literate. As a result, young people's brains are different from people that were born prior to the 1990's. Sousa asserts that part of our success as a species can be attributed to the brain's persistent interest in novelty; that is, changes occurring in the environment. 2 4 Sousa presents key points to document a comparative analysis of the environment of the past versus the environment of today. Accordingly, schools and teachers need to expedite changes that reflect what and how we teach to accommodate our changing students. This change is necessary because many students think schools are boring. These learners are consumed with spending excessive amounts of time with friends and/or engaging with some form of technology. In view of that, too many students are entering college and/or the workforce unprepared. Listed below are a few highlights: 2 5
Environment of the Past:
- The home was quieter.
- Parents and children did a lot of talking and reading.
- School was an interesting place because it had television, films, field trips, and guest speakers. There were few other distractions, so school was an important influence in a child's life and the primary source of information.
Environment of Today:
- Family units are not as stable as they once were.
- Individuals are surrounded by media: cell phones, televisions, movies, computers, video games, e-mail, and the Internet. Teens spend nearly 17 hours a week on the Internet and nearly 14 hours a week watching television.
- Many 10 to 18 year olds can now watch television and play with other technology in their own bedrooms, leading to sleep deprivation.
- The multimedia environment divides their attention.
- Young brains have responded to the technology by changing their functioning and organization to accommodate the large amount of stimulation occurring in the environment.
- Their diet contains increasing amounts of substances that can affect brain and body functions.
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