This entry discusses “Reading, Writing, and Math Brains” and the relevance of brain research to teaching and learning.
Knowledge of the structure and function of the normal brain in living human beings expanded exponentially during the last decade of the 20th century. Fueled by financial support from the United States government and advancements in brain imaging technology, neuroscientists scanned brains of mostly adults and sometimes children while they performed tasks. Likewise, neuroscientists in other countries contributed to the rapidly growing knowledge of brain-behavior relationships. Prior to this period in neuroscience history, most knowledge of brain-behavior relationships was based on autopsies of individuals who died of brain-related disease or injury.
Educational professionals expressed various reactions to this knowledge explosion, ranging from fascination and enthusiasm to skepticism. Is it really possible to go from brain scan to lesson plan? Many did not see the relevance of this basic research knowledge to their day-today practices as teachers in real-world classrooms. In part, the reluctance to embrace this new knowledge may be related to feeling intimidated by the complexity and terminology of neuroscience, which was not easily accessible by non-neuroscientists.
Typically, few pre-service or graduate students in teacher education are required to take courses on the brain as are students in medical, speech, hearing, and language sciences, occupational therapy, and physical therapy. Considering that the brain is the organ of learning, this oversight seemed shortsighted to some professionals. Virginia Berninger and Todd Richards, the authors of this entry, wrote Brain Literacy for Educators and Psychologists to introduce to educators the terminology and concepts needed to read the emerging research literature relevant to the brain and instruction and learning. Other books written for an educational audience for the same purpose are listed below under Suggestions for Further Reading. A Web site included under Electronic Resources by Eric H. Chudler is specifically directed to teachers and includes lesson plans for teaching students about their brains.
This entry provides an overview of some of what is known about reading, writing, and math brains. It also seeks to make the case that the brain and knowledge of it are relevant to teaching. Included is a brief overview of important general principals regarding the brain's role in learning and discussion of how brain research increased understanding of how reading brains, writing brains, and math brains develop as the brain interacts with the educational environment.
All learning is mediated by the brain's response to either instruction or other educational experience. Whether that instruction or experience is teacher-directed, teacher-guided (through scaffolding or questioning rather than knowledge dissemination), or self-generated and self-directed, the brain receives input from the environment. However, neither teaching nor other environmental input directly programs the brain as the software engineer directly creates programs or the computer-user enters data into the system. Rather, the environmental input indirectly exerts its effects on subsequent learning processes via the brain's attentional system, which selects a subset of the incoming stimuli for focus of attention, and the memory system, which codes the incoming information for temporary or permanent storage. Selection of stimuli for attentional focus may occur at the unconscious level in implicit memory or the conscious level in explicit memory.
The human brain codes incoming information in multiple formats depending on the physical properties of the incoming signal (e.g. visual or auditory) and existing coding formats higher in the system that are uniquely designed for
Figure 1—View from 3 Imaging Perspectives of Two Typically Developing Brains. SAG = sagittal side view of the brain section; COR = coronal frontal view of the brain section; TRA = transverse which means a top view of the brain section.
special kinds of sensory input (e.g. orthographic for visual or phonological for auditory). Working memory is a specialized brain system in explicit memory for consciously selecting, storing, maintaining, and processing incoming information and existing information in the brain for goal-directed purposes or tasks. Some of these processes may be automatic and executed in implicit memory thus freeing up limited conscious awareness in explicit working memory.
Once it is coded into working memory, further processing of the new input is influenced more by the learner's existing knowledge than the teacher's instructional input, guidance, or learning activities to foster self-guided learning. Whether the student has learned to learn, that is, created mental sets or strategies for regulating the learning process, is invisible to an observer but will determine what happens next in the learning process. However, some kinds of instruction or learning activities require that the student act on the environment, that is, produce observable behavior. The brain's motor systems are involved in such behavior generation: gross motor systems for arms, legs, body trunk or fine motor system for mouth and articulation and hand for finger movements.
How the brain mediates the teacher's instructional input or other relevant input is not directly observable, but the brain's behavioral response to that instruction is. Brain differences between students with and without developmental and behavioral problems show pretreatment differences and individual differences in response to the same instruction (e.g., Berninger & Richards, 2002). Likewise, typically developing readers in first grade instructional groups showed normal variation in response to the same reading instruction (Ber-ninger & Abbott, 1992), as did individual at-risk readers and writers (Abbott, Reed, Abbott, & Berninger, 1997).
Children probably exhibit such normal variation in response to instruction because of normal variation in the neuroanatomical structures and functions of individual brains. No two brains are exactly alike. See Figures 1 and 2. Each of these brains shown in a magnetic resonance imaging scan (MRI) has the same parts—but they vary markedly in the way the gray and white matter are organized in the convolutions (folds) of cortex on top of the brain, corpus callosum (band of white fibers connecting right and left cortex), and four ventricles filled with cere-brospinal fluid. These MRI scans are not photographs of the exquisite detail of a child's neuroanatomy but rather images that are reconstructed by computer program based on water molecules in the human brain to provide spatial information about brain structures. These scans are not invasive; that is, no radiation is used and that makes them ideal for research purposes with children and youth.
Furthermore, the brain is not only an independent variable that influences response to instruction but also a dependent variable that may change as a result of learning. In some cases the changes involve what is repre-sented—factual or procedural knowledge. In other cases changes involve how the brain functions—amount of activation in specific brain regions that vary in the physical properties of their neurons and presumable their computational capabilities.
Figure 2—fMRI Functional imaging of brain of a fifth grader deciding if words are correctly spelled real words. Significant Blood-Oxygen-Level-Dependent (BOLD) activation occurred in left cerebellum, left temporal pole, left inferior frontal gyrus, and bilateral supplementary motor area.
To summarize, the brain may influence the learner's response to instruction or learning activities, and the learner's behavior in response to instruction may in turn influence the brain's representations or functions. Teaching and learning are not synonymous—the learner may not attend to and encode into memory some or all of the environmental input from teaching or learning activities. Learning depends as much on what the brain imposes on input from the environment and operating on the environment as on the input itself. At some point in time the learner's internal learning mechanism may override the external input from teaching. As shown in the MRI images in Figure 1, the mediating brain is not a black box but rather a gray and white complex structure housed within three thin membranes inside a bony skull. General principles of organizing structure and function of this remarkable, dynamic organ are considered below.
Two general principles underlie the role of brain in learning. The first is that many different levels of analysis can be applied to the brain's structures and functions. The second is that a system approach is needed to understand how the various component functions might be organized when a brain performs a reading, writing, or math task.
Levels of Structure and Function. Brain structures and functions contribute to learning at the macro-level and micro-level. Examples of structures at the macro-level are shown in Figure 1 and are visible to the human eye. What is not visible is the labeling schemes that evolved over the 20th century to describe specific regions of interest within these structures. Some schemes use names for regions such as inferior frontal gyrus or intraparietal sulcus to indicate location of region in the four lobes of cerebral cortex: occipital, temporal, parietal, or frontal. The adjective indicates where the gyrus (ascending up like a mountain) or sulcus (ascending below like a valley) is in reference to convolutions (grey folds in cortex) surrounding the cerebrum, which contains many visible white fiber tracts (see Figure 1). Other schemes use the numbers a neurosurgeon named Brodmann assigned to specific regions, for example, Brodmann's Area (BA) 8, which is Exner's Area, one of the writing centers in the brain (for more information on the names of brain regions and structures, see Bear, Connors, & Paradiso, 2007; Berninger & Richards, 2002; Chudler Web site; and the Digital Anatomist Collection Manager Web site).
Under the microscope the micro-level of brain structure becomes visible. The basic building block of the central nervous system (brain and spinal cord) is the neuron, which consists of a cell body, dendrites that receive electrochemical signals from other neurons, and axons that send electrochemical signalsto the dendritesofother neurons. The space that separates the axon of one neuron from the dendrites of the other neuron is a synapse. The individual, microscopic neurons communicate only when an electrical impulse travels over the synapse causing the spatially separate neurons to become functionally connected for the moment until the electrical impulse subsides. Complex neurochemical events are involved in this electrical transmission (see Bear, Connors, & Paradiso, 2007, for research regarding the protein chemistry that regulates electrical transmission across synapses). The gray matter of cerebral cortex is collections of millions of neuronal cell bodies where computation occurs and the white matter of the cerebrum below isa collection of millions of axons bundled together for electrochemical transmission.
The unique computational properties of the human brain are related to this two- layer micro-level and macro-level organization. At the micro-level, spatially separated neurons communicate individually in linear time via den-drites, which look like tree branches and receive analogue signals graded in degree that are summated according to different computational mechanisms in the cell body until reaching a threshold that causes the axon to fire in a digital all-or-none manner. At the macro-level neurons containing the same parts but with somewhat different physical and functional capabilities are arranged in spatially separated cortical or subcortical regions. Large numbers of individual neurons in regional groupings with specialized computation properties communicate collectively across spatially distributed networks in the brain in multi-dimensional, non-linear, momentary time—at any moment in time the constellation of which regional groups of neurons are communicating with other regional groups of neurons varies, but their momentary spatial-temporal communication gets synthesized in real time (linear). (See Minsky, 1986, for discussion of the distinction between momentary and real time.) Thus, the human brain is an electrochemical, cross-talking network of multiple computers that communicate sequentially in time at the micro-level and in parallel at the macro-level in multidimensional space-time constellations.
The lower branches of the dendrites are under genetic control and thus influenced by inheritance and maturation, whereas the upper branches are under environmental control and influenced by education and experience (Diamond & Hobson, 1998; Jacobs et al., 1993). Consequently, the human brain develops through nature-nurture interactions to construct inner mental worlds (the mind) and overt interactions with the external world (behavior). This construction process is thought to occur through hierarchically ordered sensation (perception)-action (production) cycles with feedback and feedforward mechanisms. Without teaching and other kinds of environmental input, brains would not learn and develop, but without their internal computational mechanisms at the micro-level and macro-level, they would not learn.
System Approach to Brain Functions. Like brain structure, brain function is also complex. Alexander Luria (1902–1977), the pioneering Russian neuropsychologist, based on astute clinical observations, proposed four basic principles of organization of the working human brain for managing this complexity and creating multiple functional systems (1962, 1973):
- Many different component processing units are involved in each functional system.
- Regions distributed throughout the brain participate in any one functional system.
- Different functional systems draw on common and unique processing units (i.e. brain regions).
- Any one brain region may participate in multiple functional systems.
Having the same brain region participate in multiple functional systems and using the same common component brain regions across functional systems organized to achieve different goals lends efficiency to the fuel and energy requirements for supporting brain functions.
Brain imaging research results mesh with Luria's observations in a pre-imaging era. A consensus has developed that although certain kinds of functions tend to be associated with certain local brain regions the brain's operating system is more complex than one brain region having one corresponding function (e.g., Just & Varma, 2007). A particular brain region may be involved in more than one function and usually within the context of a neural network distributed spatially across more than one brain region. The sensory and motor processes have direct contact with the external world and code incoming information in local, primary regions, but subsequent processes draw on multiple codes, integrate them, and create more abstract representations, involving distributed space-time networks in association areas throughout the brain. Multiple, but not all, brain regions co-activate at the same time in a spatially distributed network of brain regions that are not communicating with each other constantly but rather at certain moments in time to achieve specific task-related goals. Brain functions may depend on sequences of these momentary spatial-temporal constellations being coordinated in real time, much as an orchestra conductor creates music by keeping the individual musical instruments, which do not all play at the same time, playing in temporal synchrony across time (Posner, Petersen, Fox, & Raichle, 1988).
Temporal Coordination of Components in Functional Systems. Fuster (1997) devoted his career to studying the frontal lobe, which is larger in humans than other species, especially in dorsal lateral prefrontal cortex (DLPFC), and houses executive functions, including but not restricted to temporal coordination. Based on a life-time of empirical studies, many with white rats, he proposed a model of cross-temporal contingencies for orchestrating the component processes of functional systems in time. The model has three networks:
- A bottom-up pathway that originates in the sensory areas in the back of the brain that have direct contact with the external world and project incoming information to the association areas that do not have direct contact with the external world;
- A top-down pathway that originates in the abstract association areas of DLPFC in frontal lobe and projects to midlevel premotor and supplementary motor cortex and then on to primary motor cortex (all in frontal lobe) and finally to spinal cord that generates the elements of movement that act on the world;
- A cortical-subcortical pathway (including the cerebellum below the cortex and behind the cerebrum that has about half the neurons in the brain) for temporal coordination of the sequential and simultaneous communication of the other pathways.
Working Memory Component in Functional Systems for Reading, Writing, and Math. A common subsystem in the functional systems for reading, writing, and math functions is the working memory system that supports conscious, goal-directed behavior. Working memory is thought to consist of storage and processing units coordinated through a central executive (e.g., Baddeley, Gath-ercole, & Papagno, 1998; Swanson, in press). Although the phonological loop was first proposed as a mechanism for maintaining information over time in working memory, it has also been investigated for its role in regulating language learning involving overt or covert naming (e.g., vocabulary words that involve cross-code mapping of visual codes, name codes, and concept codes) (Baddeley et al., 1998). In addition, recent evidence for an orthographic loop for integrating orthographic codes and grapho-motor codes for output by hand was mounting (e.g., Beringer, Raskind et al., in press).
Fuster (1997) proposed implications of his model for working memory. The bottom-up sensory pathways may play an important role in coding and storing incoming information in working memory. The top-down pathway emanating in the dorsolateral prefrontal cortex (DLPFC) may play an important role in the central executive processes of working memory, including supervisory attention and self-regulation of acts upon the world during task completion. The cortical-subcortical pathway may contribute the temporal coordination of the executive functions coordinating codes and/or processes. The cortical path involves DLPFC, including middle frontal gyrus, and the subcortical path includes the cerebellum.
Because working memory is a critical component of all reading, writing, and math brains, this entry focuses on its possible brain basis in creating reading, writing, and math brains through nurture-nature interactions as the learning brain interacts with the external, learning environment. A word of caution is in order. In the initial studies of academic learning during the Decade of the Brain, the focus was on identifying regions of interest that were associated with particular cognitive functions (and presumably computations). Although much progress was made on this front, it is increasingly clearinthe early 2000s that academic skills such as reading, writing, and math draw on neural networks distributed in space-time constellations throughout the brain and increasingly brain imaging researchers are studying the temporal connectivity of distributed networks or the temporal unfolding of neural events in complex functional systems rather than focusing on a single region of interest (e.g., Richards & Berninger, 2007; Shaywitz et al., 2003; Stanberry et al., 2006). Moreover, localizing a function to one brain region does not explain a learning process; it merely pinpoints where some of the action is.
How the brain works is not yet fully understood. For one thing, language processing, which is needed for learning to read, write, and do math, activates both right and left cortical regions. Is the side of the brain activated related to the nature of code for the stimulus storage or processing or to one hemisphere (side of cortex and cerebrum) taking the lead and the other inhibiting networks in the same structure on the other side? When some neurons fire, the electrical signal travels across the synapse causing the receiving neuron to fire in turn or not to fire. The first kind of neuron is excitatory, and the second kind of neuron is inhibitory. Up to two-thirds of the neurons in the human brain may be inhibitory. Children who fail to learn or behave appropriately may not choose not to learn or behave appropriately; rather, they may have neurons that have not yet myelinated, that is, formed a white sheath of myelin that improves the speed and efficiency of neural conduction in networks supporting inhibition and/or excitation.
Thus, the next section of this entry will not, for the most part, identify a single brain region of interest for each function, but rather will offer a conceptual model for a system of component processes that involve local brain regions in distributed spacetime networks, which when coordinated in working memory achieve reading, writing, or math goals. Teachers may find this conceptual model useful in thinking about individual differences in learners who vary in where they have their strengths and weaknesses in working memory components and the related instructional implications. For each content domain, codes represent and store incoming domain-specific information, loops integrate codes with end organs for input and output, and executive functions manage working memory components supporting conscious, task-oriented functions; these working memory components are in boldface in Tables 1, 2, and 3. This working memory architecture is necessary but not sufficient. Issues also considered are (a) other processes supported by working memory to reach goals, (b) the previously discussed three cross-temporal contingencies, and (c) the distinction between internal cognition in invisible/inaudible working memory and external cognition, a kind of extramemory in the visible/audible external world. Coupling internal working memory and external cognition may facilitate learning (Winn, Li, & Schill, 1991).
This section illustrates how each of the working memory components contributes to development of a functional system for a reading brain.
Codes and Storage. To learn to read, children must code written words and letters into working memory; this code is called orthographic word-form. The goal is to translate that orthographic word-from into a spoken word (phonological word-form). Once children hear what is pronounced, that spoken word is then coded as an audible phonological word-form that provides sensory feedback about the sounds in the word. When children master the decoding process of translating written to spoken words, they no longer need to read aloud for this phonological feedback which is now accessible through inner speech (covert sound code that is not audible but codes the phonemes that correspond to alphabet letters, that is, alphabetic principle). Both the orthographic and phonological word-form may also have morphological structure (base word plus prefix and/or suffix/es), which the reader may also code. See Table 1.
Processing. Written words are accessible for processing once they are coded as orthographic word forms. Two kinds of cross-word form processing—fast and slow— may convert orthographic word-forms into phonological word-form (and morphological word-forms). Both are regulated by the phonological loop for cross-word form integration via the act of naming the whole written word or part of it, thereby, making a close-connection in time between an orthographic and phonological code. The codes are probably stored and processed in word-form regions in the back of the brain (e.g., fusiform gyrus, lingual gyrus, inferior temporal gyrus) and may be integrated in Brodmann's Area (BA) 37. Wernicke's Wort-shatz (treasure house for words) (see Berninger &
Richards, 2002) outside the primary visual areas; but larger temporal-parietal (and visual association areas of occipital) regions are likely to be involved too (Pugh et al., 1996). The phonological loop may involve a right cerebellar-left inferior frontal gyrus network (Eckert et al., 2003; Richards et al. 2006b). Developing reading brains need instructional activities for both fast mapping and slow mapping (see Table 1).
Fast mapping occurs from one or a few exposures (McGregor, 2004), in this case to a seen written word and a heard spoken word close in time, forming a connection between them through association. Once the cross-word-form map is completed, the child automatically recognizes the word, that is, can pronounce it or recognize it through inner speech. Teachers often refer to words learned through fast mapping as sight word vocabulary, but orthographic and phonological codes are involved not just primary visual regions of brain. Orthotactics (permissible letter sequences and letter positions in words) and phonotactics (permissible sound sequences and sound positions in words) may underlie ease of learning to read as well as spell (see Apel, Oster, & Masterson, 2006) through fast mapping. Some children may struggle with automatic word recognition because of undiagnosed and untreated phonotactic and/or orthotactic problems.
Slow mapping requires a longer learning period and involves more refined units of correspondence between two codes (McGregor, 2004). This slow mapping, which typically requires explicit instruction to bring the corresponding codes to the child's conscious attention, benefits from teaching multiple connections between graphemes (one- or two-letter units) and phonemes (the sounds inspoken words that correspond to alphabet letters); written rimes (part of the syllable remaining when onset phoneme or blend is deleted) and spoken rimes; syllable types (closed, open, silente, vowel teams, r- controlled, and the -le syllable; and morphological structures for transforming base words by adding prefixes or suffixes. The first kind of slow mapping is the alphabetic principle that is fundamental to phonological decoding of written words. The second kind of slow mapping is word families, which also benefit phonological decoding, especially when the orthographic-phonological correspondence is more predictable for multi-letter units that may exceed two letters (e.g., -ight in right or light). Mapping syllables by classifying them has been found to be more helpful than teaching children to merely mark where one syllable ends and another begins because in English syllable boundaries can be altered by the speed at which a word is said. The morphological mappingiscritical for developing vocabulary meaning and a bridge from cross-code word maps to the text-level comprehension processes (e.g., Nagy, Berninger, & Abbott, 2006; Nagy, Berninger, Abbott, Vaughan, & Vermeulen, 2003). Although many children acquire these maps during the first three grades, others require a longer period of explicit instruction in slow mapping well into middle school and even high school years, possibly because of individual differences in the rate of myelination already defined.
Executive Functions. Frontal and subcortical cerebellar regions and the many neural pathways among them and the anterior cingulate (a region involved in conflict management) play important roles in regulating the process of learning to read and then reading to learn: Lower-level executive functions, especially inhibition and switching attention (Altemeier, Abbott, & Berninger, 2007) but also maintaining attention over time (Amtmann, Abbott, & Berninger, 2006). Inhibition is the ability to focus on what is relevant and suppress or ignore what is irrelevant. Switching attention is the ability to release from focus of attention what was relevant and switch to what is now relevant. Maintaining attention isthe ability to stay focused over time for goal-directed activity, especially when orthographic-phonological code integration is involved. Children who struggle with reading may have difficulty with any of these (Altemeier et al., 2007; Amtmann et al., 2006). Executive functions involving supervisory attention influence orthographic word-form processing (Thomson et al., 2005). Teachers can incorporate in lesson plans, for those children who struggle with attention regulation for written words, strategies for focusing on the relevant, switching attention focus, and maintaining attention over time.
Higher-order executive functions are also involved in reading such as verbal fluency (word finding) and linguistic awareness (see Table 1). Readers need to find in long-term memory associated names (phonological word-form) and meanings for written words. Long-term memory stores complex cognitive representations in associational networks or webs, hierarchical, categorical classification systems, and nonverbal visual images (see Stahl & Nagy, 2005). They also need to reflect upon the word-forms and their parts to develop orthographic awareness, phonological awareness, and morphological awareness (see Berninger & Richards, 2002, Chapter 8).
Other Processing Jobs. If the task is to comprehend the written text, accurate identification of single written words is necessary but not sufficient. Syntax emerges during the preschool years for storing accumulating words in working memory for the purpose of comprehending the incoming oral language message; the sum is greater than the parts in the syntactic constructions based on single words. Children who have problems with ordering accumulating words in working memory according to the syntax structures of the language may have problems in comprehending both oral and written language and persistent reading comprehension problems during the school years (Berninger, in press). However, reading comprehension depends on many levels of language, ranging from vocabulary meaning for single words or idioms of the language to sentence syntax structures to discourse schema (see Table 1). Many parts of the brain are involved in reading comprehension both in the back of the brain (e.g. Wernicke's Area) and front of the brain (e.g. DLFFC and superior frontal gyrus) (see Ber-ninger & Richards, 2002, Chapter 5).
Top-down, Bottom-up, and Cortical-Subcortical Temporal Coordination. Both learning to read and reading to learn require engagement of the bottom-up system (incoming visual information from the written text that proceeds upwards in the system to be coded for orthographic, phonological, and morphological word-forms, syntax, and semantics—the links between language and cognition), the top-down system (existing factual and conceptual knowledge in long-term memory from life experience and prior reading as well as cognitive procedures for abstracting the gist and details from incoming text and summarizing what is read), and cortical-subcortical temporal coordination (the grand orchestra conductor of mind for coordinating all the processes in momentary and real time).
Even if purpose-setting questions and discussion of background knowledge (top-down processing) precede the actual act of reading written text, the initial process in the actual reading begins with bottom-up brain processing initially in visual cortex but subsequently in temporal-parietal-frontal networks. At some point in this process, top-down and cortical-subcortical temporal coordination processes activate and can influence reading outcomes.
Internal and External Cognition. Input codes that are not exclusively visual and several output codes may externalize cognition in ways that support internal working memory during reading. The first are ocular motor codes that regulate eye movements as the eyes move forward, then backward, and then pause to fixate on external word information whileitisbeing processed; see Berninger and Richards, 2002 for the multiple central (brain and spinal cord) and peripheral (outside brain and spinal cord) regions of the nervous system involved in eye movements. The second is the mouth's oral-motor system that turns written language, which is originally only visible, into audible language, that is, one's first language. That is why oral reading provides important external feedback in learning to read written language. The third is nonverbal cues, including vocal cues (the intonation or musical melodies of spoken language) and bodily expression that may facilitate the translation of written into oral language. For example, some students who struggle to read textbook text orally become fluent when reading play scripts allowing them to act out concepts underlying language and drawing on the intonation of oral language. The fourth is grapho-motor codes that support writing words by hand. Spelling words in writing transferred to improved word reading; and written composition instruction may benefit reading comprehension (e.g., Ber-ninger, 2008). The postcentral gyrus (primary somatosen-sory area in parietal lobe) receives information from the environment through touch and kinesthetic movement via hands engaged in writing-related reading activities. This somatosensory stimulation may be transmitted to nearby supramarginal gyrus (a phonological processing center) through explicit phonological activities involving hands (e.g. counting syllables or phonemes and writing letters that go with phonemes or hands-on, science problem-solving activities with virtual reality) (Richards et al., 2007).
Writing has many component processes (see Table 2), but most brain imaging has been done on transcription skills (handwriting and spelling). Acquired writing disorders in adults are associated with three brain regions: (a) left posterior middle frontal gyrus (Exner's Area BA8) (Exner,1881) thought to support coactivation of movement sequences during letter generation (Anderson, Damaisio,& Damaisio, 1990); (b) left superior parietal lobule where internal letter codes are thought to form for production (Basso, Taborelli, & Vignolo, 1978); and (c) left premotor (BA6) thought to store the grapho-motor codes for writing letters (Brain, 1967). A close relationship exists between letter production and letter perception—both motor and visual regions are involved in handwriting (James & Gauthier, 2006; Longcamp et al., 2003).
At the end of fifth grade good and poor writers, who differed significantly on behavioral measures of handwriting and spelling, also differed significantly in blood-oxygen-level-dependent (BOLD) activation in each of these regions identified for acquired writing disorders during a functional magnetic brain imaging (fRMI) Finger Succession task controlled for non-successive finger tapping (Richards et al., submitted 2008). In that same study, the good and poor writers differed significantly in left fusiform gyrus in lower non-motor temporal regions on a Handwriting Contrast between a novel configuration and a familiar letter equated for motor movements in formation; fusiform codes letter forms, showing that handwriting is not just a motor skill. Prior findings from two studies with adult writers (Matsuo, Kato, Ozawa et al., 2001; Matsuo, Kato, Tanaka et al., 2001b) replicated for children. Both the good and poor writers activated fewer brain regions when a letter form could be phonologically coded (associated with a phoneme) than when it could not. Alphabetic principle for mapping graphemes onto phonemes may have a brain advantage for more efficient letter writing.
Brain imaging of normal adults during spelling tasks showed that orthographic word-form activated inferior temporal (e.g., fusiform) more robustly than primary visual (occipital) regions in response to linear arrays of visual elements that can be linguistically coded (e.g., Cohen et al., 2002; Dehaene et al., 2002). Phonological-orthographic mapping activated left fusiform gyrus (Booth et al., 2002), posterior parietal cortex (Bitan et al. 2007), and left inferior frontal gyrus (Booth et al., 2007). The time course proceeded from occipital visual association areas to Wernicke's Area (cross-code integration), to left inferior frontal gyrus (Dhond et al., 2001). For the good spellers in grades 4 to 6, significant BOLD activation during an fMRI spelling task occurred in medial superior frontal gyrus, bilateral middle frontal and inferior frontal gyri, middle temporal, fusiform and lingual gyri, right orbital and posterior parietal regions, left superior temporal and inferior temporal gyri, and anterior cingulate and anterior insula, (Richards et al., 2006a). Two conclusions can be drawn—spelling like reading is not a purely visual process and the temporal and parietal regions involved in orthographic and phonological word-forms and their integration appear to activate word-form regions during spelling as well as reading in children. Also, the inferior frontal gyrus involved in the highest level of executive function for coordinating the language systems is activated in brain during spelling as well as reading in children.
Prior to treatment, good and impaired spellers differed significantly in BOLD activation in right inferior frontal gyrus and right posterior parietal BOLD activation, but after orthographic (not morphological control) treatment, the poor spellers normalized in both regions compared to good spellers (Richards et al., 2006a). Based on common core and unique BOLD activation across phonological, orthographic, and morphological wordform tasks (e.g., Richards et al., 2006b), Richards et al. (2005) compared two of these at a time to identify common core and unique brain activation underlying phonological-orthographic, orthographic-morphological, and phonological-morphological mapping in children aged 9 to 13. Results showed a common core of many brain regions and a sizable number of uniquely activated brain regions more associated with one word-form than the other. Clearly, large distributed networks involving many language areas are involved in cross-word form mapping of phonological, orthographic, and morphological word-forms in spelling in children. This cross-word mapping may begin in the posterior word-form centers in temporal-parietal regions and culminate in the left inferior frontal gyrus for phonological mapping and the right inferior frontal gyrus for orthographic mapping (Richards et al., 2005).
Figure 2 shows an individual fifth grader's brain while deciding whether each of two words (always pronounced the same) were real, correctly spelled words. All components of a working memory architecture showed significant BOLD activation: a left temporal region for orthographic word-form and phonological word-form storage and processing, left cerebellum that may be involved in orthographic for cross-code integration in spelling, and two frontal regions (one on left associated with executive functions for language and the supplementary motor area involved in motor planning on both sides).
Top-down, Bottom-up, and Cortical-Subcortical Temporal Coordination. Writing is not the inverse or mirror image of reading (Read, 1981). Note that different component processes are at the top of Table 1 and top of Table 2 for reading and writing, respectively. Also see Chapters 8 and 9 of Berninger and Richards (2002) for further discussion of the differences between the developing reading brain and the developing writing brain. Instead of beginning like reading with a bottom-up pathway, writing begins with a top-down pathway during idea generation and goal-setting of the planning/proposing processes (Hayes & Flower, 1980; Hayes, in press); Good writers and poor writers at the end of fifth grade differed in BOLD activation in the superior and middle frontal gyri (including DLPFC) while their brain was scanned during fMRI Idea Generation; when they left the scanner, they wrote compositions on what they learned during the summer that they had not learned in school (Berninger et al., 2008). Where they differed suggested that good writers engaged working memory more than poor writers as early as idea generation that initiates the writing process.
Processing. Cognitive processes such as planning, translating (ideas into language), transcribing, and reviewing and revising are important throughout the writing process of skilled adults (e.g., Chenoweth & Hayes, 2001, 2003; Hayes, 2004, in press; Hayes & Flower, 1980), and some progress has been made in how to teach these cognitive processes effectively to young children and middle school students (for review, see Berninger, 1998). Translating occurs at many different levels of language ranging from letters to words to sentences and discourse structures (see Table 1). Additional research is needed to determine whether all these translation processes occur simultaneously or sequentially or both or depend on expertise level and writing purpose.
Codes for Storage and Mapping. In contrast to reading that maps orthographic word-forms onto phonological word-forms, writing maps phonological word-forms (spoken or analyzed with inside voice) onto orthographic word-forms. Like reading, the mapping may be fast or slow and fast mapping may be influenced by phonotactic and ortho-tactic knowledge, as defined in reading section. English spelling is hard because slow mapping has more alternations or possible spellings for a given phoneme than possible sounds for a given one- or two-letter grapheme (Venezky, 1970, 1999). Both the phonological and orthographic word forms may also have morphological structure. In the case of writing, these morphological structures for transforming base words by adding affixes (Carlisle, 2000) may facilitate word choice during the text generation process, which like reading, occurs at multiple levels of analysis ranging from word to sentence to discourse schema (see Table 2).
Executive Functions. Writing is more complex than reading because it places more demands on executive functions (e.g., Hooper et al., 2002). In addition to low-level executive functions in frontal and cingulate regions, high-level executive functions are required such as (a) planning that involves both idea generation and goal setting for tasks requiring space-, time-, and resource-limited conscious working memory, (b) translating cognitive representations into linguistic representations at multiple levels of written language and translating those levels of language via transcription into written symbols, and (c) reviewing (self-monitoring) text produced and revising it as needed (not only surface feature edits but also repairing deep structures through substantial rewriting).
Internal and External Cognition. The executive juggling act of writing may place greater demands on internal working memory than reading does, but writing has the advantage that it externalizes cognition making it visible via written language to become an object for reflection and repair. Moreover, learners often do not have access to what they are thinking in implicit memory until it becomes consciously available through writing in explicit memory and externalized cognition (see Hayes & Flower, 1980).
Brain imaging studies with adults produced mixed results when localized regions for coding operations during math were investigated, but they clearly support a major role for the parietal cortex and the representation of an internal number line that codes quantity; exact and estimated math appear to be represented in different neural networks. The math brain draws on many of the regions that reading and writing do because math involves verbal as well as quantitative and visual spatial representations and procedures. However, one brain region uniquely involved in the math brain but not the reading or writing brains is the lenticular nucleus (for review of imaging studies in math and instructional implications, see Ber-ninger and Richards [2002, Chapters 7 and 10]). Math, which has many branches and subspecializaitons, begins with the concepts underlying this knowledge domain.
Concepts. Counting is the fundamental cornerstone of math in early math development and the work of mathematicians engaged in discovery of mathematical truth (see Hoffman, 1998, for account of Erdös the mathematician who loved only numbers). Numbers can extend in either direction infinitely and be real or imaginary. Some mathematicians devote their careers to detecting complex patterns in the number line that are then used to solve important problems about the physical universe. Multiple number lines (one for each continuous dimension) can be used to describe quantitatively how changes in one distribution affect changes in another distribution and to solve problems involving multiple number lines, each on different scales (e.g., seconds, minutes, hours, half days for telling time). Another key concept is place value, which is the syntax for numbers and allows the math brain to represent an infinite number of numbers with just ten symbols if one of them is zero to indicate nothingness. The part-whole concept is another cornerstone of math underlying fractions, mixed numbers, telling time, measurement, and algebraic reasoning. Children first learn that objects have permanence in the mind even if not in the external world and then they must learn that quantity for objects is not absolute—the magnitude depends on how many parts the object has. One-fourth is less than one-half no matter what the absolute size of an object even though four is a larger quantity than two (see Table 3).
Codes and storage. A number is an internal representation of quantity, that is, a quantitative code, abstracted from counting many objects, but a numeral or digit is an external symbol written by hand for that number by the grapho-motor system and is visible to primary visual area of brain. Numbers also have names that stimulate the primary auditory area and are audible to the brain. Letters and numerals may be represented indifferent locations in brain (Anderson et al., 1990) even though grapho-motor codes for writing them may be the same (see Table 3).
Processing. Arithmetic is often confused with mathematics, which is higher-order problem solving, including proving theorems and applying science to the physical universe and human behavior. Arithmetic involves number facts (learning them and retrieving them are separable processes), and arithmetic algorithms for calculation (steps of basic addition, subtraction, multiplication, and division operations). Math fact learning and retrieval and calculation operations may be executed in internal working memory (mental math) or coupled with the external environment through written calculation (see Table 3).
Executive Functions. All low-level supervisory attention functions influencing reading and writing brains may also influence the math brain. In addition, math calculation and problem solving require planning, thinking, translating metaknowledge about math, and self-monitoring and correction.
Top-down, Bottom-up, and Cortical-Subcortical Temporal Coordination. Math problem-solving typically initiates with top-down pathways, but math fact retrieval and calculation may begin with bottom-up pathways. As with the reading and writing brain, the math brain requires orchestration in time of all the relevant processes to the task at hand (see Table 3).
Internal and External Cognition. Hand-held calculators and other technology tools provide external cognition support for overcoming weaknesses in internal working memory that support math problem solving. However, unless math is taught in a way that includes mental math as part of the coupling of working memory and external cognition supports, learners will never become skilled in math. Ultimately mathematical thinking and applications occur in the math mind—the math brain at work.
Knowledge of the developing brain and its influences on learning to read, write, and do math is not absolutely necessary for individuals to be effective teachers for many students. Such knowledge may matter for designing and implementing specialized instruction for students with biologically based developmental and learning disorders and for optimizing academic achievement of all students. Working memory components and other processes in Tables 1, 2, and 3, may break down or be a talent in individual students. Whether such knowledge translates directly to daily lesson plans may depend on teachers' grasp of the whole system of processes involved in learning and not just teaching reading, writing, and math and individual differences among learners that affect response to instruction. At a time in the history of education when educators are becoming aware of diversity due to multicultural backgrounds of learners, it is equally important to understand that biodiversity is also relevant to academic achievement.
Students may differ in meaningful ways in the kinds of learning environments in which they learn most appropriately. Educators and students need a no-fault approach to education. Academic underachievement cannot be attributed only to teachers or only to students. Not all students learn the same way and learning is harder for some than it is for others because of brain differences. Improving teachers' knowledge of the brain may lead to greater compassion for learners who do not learn easily and may stimulate teachers to discover creative alternative instructional approaches for improving the match between how individual students learn and the environmental conditions under which they may realize their biologically influenced talents and overcome their weaknesses. Increasing pre-service teachers' knowledge of brain and biodiversity along with multicultural diversity may contribute to this next step in educational evolution that leaves no teacher or student behind (see Berninger & Richards, 2002, Chapter 12).
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