Despite what many believe,learning isn’t simply the mentalact of adding to what wealready know. It’s the mentalact of reformulating — morphing, so to speak —what

we thought we knew into somethingnew and different that might be moreinclusive, or more specific, or some-thing that under a banner of differentdescriptions involves new ways ofthinking. Learning occurs through con-ceptual change, a phenomenon that canbe described through constructivistlearning theory.

But constructivism is controversial.It is cited as the fundamental theoreticalbasis of position statements and learning standards published by manynational educational associations, suchas the National Council of Teachers ofMathematics, the National ScienceTeachers Association, and the NationalCouncil of Teachers of English, to namea few. However, it is also targeted bymany political groups as the reason whyJohnny and Jane “can’t.” Why they can’t read, can’t compute, can’t recallhistorical events, can’t locate cities on a map ... just can’t.

The Controversy

So, what is so controversial aboutconstructivism? Constructivism is thetheory that learners generate meaningthrough the active mental process offormulating and reformulating knowledge. Broadly, this frameworkstands in contrast to other assertionsthat the learner’s mind is a clean slateready for inscription through directinstruction, or an empty vessel ready tobe filled by the instructor. After all, it’smuch easier to think of learners asblank slates or empty vessels than aseveryday theoreticians with intellectualautonomy who formulate, reformulate,and reformulate ideas yet again. It’s easier to think of education as “testthem, teach them, and test them again,”than as a process essentially controlledby the learner and mediated by theteacher. The controversy about con-structivism is rooted in the debate overhow people learn (and, therefore, howteachers teach), with some attributingthe power to learn to the learner, andothers attributing it to the teacher.

HOFSTRAHORIZONS13

Thinking About Learning

Jacqueline Grennon BrooksAssociate ProfessorDepartment of Curriculum and Teaching

Second graders noticing the soapy water on the blackboard evaporating! Hofstra graduate student Karyn Lundgren, pursuing an M.A. in math, science and technology, studied children's conceptions of the water cycle.

HOFSTRAHORIZONS14

Constructivism has become thelightning rod for critics of progressiveeducation because of their contentionthat in constructivist classrooms, basicskills (for example, calculating the cir-cumference of a circle using a formula)seem to take a back seat to larger con-ceptualizations (for example, the rela-tionship between the circumference ofany circle and its diameter consistentlybeing a little greater than 3:1, regardless

of the size of the circle, π:1, to be moreprecise!). But, the general public doesnot well understand the relationshipbetween the ability to compute effective-ly and the ability to understand theessential relationships that give rise tothe formula used in the computation.This is why it often appears to criticsthat the curriculum is being watereddown and that teachers spend too much

time on ideas that don’t really matter.But, neither is true. To the contrary,there is research (TIMSS, 1995, 1998,2003; NAEP, 1999) showing that stu-dents taught math and science in the so-called “traditional” ways often performin the fair to poor range on national andinternational measures of success, thevery type of measures used as indicatorsof success of basic skills teaching.

Perhaps Johnny and Jane “can’t”because schools have become quite pro-ficient at doing the wrong things withstudents. When learning is thought tobe the result of meticulously scripteddelivery systems, prescribed curriculaand regulated assessment systems,rather than the making of meaning bythe learner, Johnny and Jane spend theirtime following directions and getting“right” answers rather than experiment-

ing, being wrong (and right, too), andlearning from their own errors.Sometimes Johnny and Jane spend theirtime on activities that, on a glance, looklike they’re part of a constructivist class-room, but aren’t. For example, studentsin a traditional class might build modelstructures of different types of bridges inorder to investigate different types offorces. In these classes, students design,build, weigh, and load the models untilthey collapse. There are many of theseclasses in which the tumbling of thebridges signals the end of the activityand thus, the end of the thinking. Inthese settings, students often focus onlyon who had the “best” bridge.

On the other hand, constructivistclassrooms that offer opportunities forrich learning require teachers who canextract basic, organizing principles and

Bernel Connelly-Thomas, a Hofstra graduate student, studies children's conceptions of surface tension by guiding them in their observations of swirling food coloring in milk.

HOFSTRAHORIZONS15

content from student inquiries (Bakerand Brown, 1991; Hawkins, 1992). Inthe constructivist classroom, the lessondescribed above only begins when thebridges tumble. The purpose of thebridge building is to provide a contextu-al problem in which the teacher situatesthe learning of patterns. The teachermight encourage students to identify thegeneric designs represented, supportstudents in their attempts to group thedesigns, challenge students to considerwhat these groupings imply aboutforces, provide resources for students tocompare their results with other pub-lished sources, foster the selection ofappropriate text material for furtherinformation, and facilitate student docu-mentation of results. These teacherprompts foster pattern recognition. Atthe end of the research, the teachermight ask the students to build anotherset of bridges, and compare the per-formance of the new set to that of theprevious set. Within this scenario, thestudents demonstrate their capacities toexplain their reasons, thereby exhibitingwhat they have learned.

Pattern Recognition Is Key inConstructivism

The study of pattern recognition,described as learners’ quests to map rela-tionships among parts of a concept, andto group those relationships into ever-more inclusive mental structures, hasbecome increasingly noted within theresearch literature. There are many stud-ies pointing to the importance of patternfinding. For example, the large-scaleARC Center Tri-State StudentAchievement Study (2000-2001) exam-ined the performance of students usingthree elementary mathematics curriculabased on constructivist theory that weredeveloped and researched through theNational Science Foundation. While eachof the curricula takes a unique approach,all three, to varying degrees, invite youngstudents to study mathematics as a pat-tern-finding science, stressing communi-cation of mathematical content throughcritical literacy, and building teacher

knowledge of how students learn mathe-matics. Not surprisingly, it was foundthat students in classrooms using thesecurricula consistently outperformed thecomparison students on a number ofstate standardized achievement tests.These significantly higher average scoresheld true across grade levels, reading lev-els, SES, racial/ethnic identity and othervariables. In another example, two well-known science curricula generated at theLawrence Hall of Science at theUniversity of California in Berkeley focusbroadly on pattern recognition, andresearch on those programs report stu-dent transferability of skills, among othersuccesses (Klentschy, Garrison, &Amaral, 2001; Franklin-Leach, 1992;Jones, 1990). It is hypothesized by thisauthor that pattern recognition facilitatesthe mental self-regulatory strategies thatresult in conceptual change, with contin-ual conceptual change resulting inincreasingly complex thinking.

Learning About Learning

Do students interacting with teachers who foster the discernment ofpatterns learn to seek efficiency in theself-regulatory strategies that producecomplex thinking? This research question brings us closer to the core oflearning about learning and providesopportunities to create educational environments based on new understand-ings (See Figure 1). How close we canget to understanding complex thinkingon the neural level is an open question,and beyond the scope of our currentefforts. We hope to answer these questions in the future by forming professional alliances within the neuro-science and educational communities,by creating clear research protocolswithin these alliances, and by relying on the future development of instru-mentation in the imaging field.

Jill Greismeyer, a Hofstra graduate student, studies children's conceptions of density by inviting them to make their own salad dressing.

HOFSTRAHORIZONS16

Still, there are many exciting devel-opments already underway. Currentneuroscience research uses a number ofmethods to detect brain activity. Theprocess of using sensors to detect themagnetic field created as brain cellscommunicate is called magnetoen-cephalography (MEG). Recent advancesin instrumentation and the present daydesign of the helmet-shaped magne-tometer used in MEG studies haveallowed for a number of new under-standings of brain function by combin-ing the temporal information gainedthrough MEG with the structural infor-mation gained through magnetic reso-nance imaging (MRI.) Although newand very promising understandings ofbrain function are being generatedthrough MEG and functional magneticresonance imaging (fMRI), we are notready to apply this technology to brainmapping studies useful to teachers. Anumber of technological and researchprotocol advances must be made to takethe step from generating the types ofbrain maps available today to generatingtypes that may, or may not, in thefuture, link teaching strategies withbrain cell activation. Alliances betweenresearchers conducting cognitive science

investigations on conceptual change andresearchers conducting brain-mappingstudies of brain cell communicationcould set the stage for a new era inlearning about learning. Imagine being

able to compare brain cell activity dur-ing lessons requiring rote computationversus complex problem solving! Notinsignificantly, these advances inresearch may someday offer neurologicalevidence of the power of constructivistpedagogical approaches.

Studying Concepts, Mapping Patterns

But back to today’s research andtoday’s classrooms. It is widely recog-nized that what students learn in schoolis rarely generalized into applications,theories and principles subject to further investigation. Therefore, deepunderstanding is often absent and, withit, a basis for reasoning and explanation(Schoenfeld, 1988). In order to furthereducational practice targeted at promoting pattern recognition and also generate a research approach that studies learners’ pattern recognition and conceptual change, the ThinkingMapsTM language (Hyerle, 1996) is auseful tool (See Figure 2). This languagehelps the teacher look for and find patterns within the concepts under

Figure 1. Conceptual Framework

Andrea Schmidt and James Ufier, Hofstra graduate students, exchange some laughs as they use apples and oranges and the very air around us tostudy children’s conceptions of the process of oxidation.

HOFSTRAHORIZONS17

study for him/herself, helps the teacherreplicate that opportunity for the stu-dents in his/her classroom, and providesa vehicle for the collection of data onstudent pattern finding. The thinkingmaps are based on the theory that thereare fundamental cognitive skills that canbe dynamically represented throughvisual mapping.

The Thinking MapsTM constitute acommon visual language that teachersand students can use, either independ-ently or within cooperative structures,for making sense of stored knowledgeand for building new concepts, linearand nonlinear. Each of the eight maps

can help a thinker generate new ideas,consistently organize those ideas, andprocess them on a deep and dynamiclevel. The simple maps, called graphicprimitives, can be configured into moreelaborate ones. Each map is associatedwith a fundamental cognitive skill, andeach provides a language for cognitiveterms: representation of context,description of attributes, comparisons/contrasts, inductive/deductive classification, part/whole relationships,sequences, cause/effect, and analogies.These maps are effective, and approxi-mately 3,500 whole school faculties,mostly at the elementary school level,

use thinking maps in their educationalprograms. As a result of their use, initialcase studies report increased recall ofcontent when reading, greater capacityto communicate abstract concepts, and the transfer of thinking processeslearned in one setting to another(Hyerle, 2004).

As described by Donald Stokes inPasteur’s Quadrant (1997), research onstudent learning must occur in the natural settings of schools because onlythere is it use-driven, systematic andstrategic. In his book, Stokes eloquentlymakes the case for needing to fuse twotypes of research: research to understandthe nature of learning, and research toapply learning principles to practice. Inorder to document student learning thatis correlated with the nature and development of pattern recognition, thestudent learning being researched musttake place within an environment thatfosters such processing. As recommend-ed by the National Research Council inits important book How People Learn(2000), the fusion of research and practice through professional learningcommunities provides pathways forteachers to re-frame practice based ontheir own action research, research thatcontributes to understanding theprocesses by which learners constructmeaning from the objects, texts andphenomena of everyday life and of educational settings.

Using a wide range of research toolsin both traditional and innovative set-tings, many of us within Hofstra’sDepartment of Curriculum andTeaching seek to address the essentialneed to better understand and morefully implement methods of teachingconsistent with what we know aboutlearning. Within many of Hofstra’sundergraduate and graduate teachereducation programs, novice teachersparticipate in action research endeavors.They generate essential questions andcontinually revisit hypotheses as theyexamine their practices, monitor theimpact of student understandings andobserve the expansion of learners’ repertoires of knowledge to expanded

Figure 2. Thinking Maps as an Educational Tool

Jacqueline Grennon Brooks’ interest inhow people learn began with her first job as asixth grade teacher and has led to her currentstudy of the role that pattern recognition playsin conceptual change. Dr. Grennon Brooks’education is diverse, and includes an Ed.D.from Teachers College, Columbia University,where she researched the development of con-structivist teaching practices; an M.A. in devel-opmental psychology from Teachers College,Columbia University, where her study of con-

structivism began; an M.S. in urban and policysciences from the State University of New Yorkat Stony Brook, where she analyzed mathemat-ical forecasting models at the CongressionalBudget Office; and a B.A. in education fromthe State University of New York at StonyBrook, where she learned just how complexteaching really is!

Dr. Grennon Brooks has been studying learningprocesses for many years and has writtenwidely on the subject. As an advocate forchange in today’s educational system, she is afrequent contributor to school districts and edu-cational associations. Her 1993 book, InSearch of Understanding, the Case for theConstructivist Classroom, co-authored withMartin G. Brooks, has been translated into fourlanguages and continues to be one of the pub-lisher’s best sellers. Her recent book, Schoolingfor Life: Reclaiming the Essence of Learning(2003), has received highly positive reviews inthe field. Her work, cited in many texts andmultimedia programs, was recently selected bythe National Science Teachers Association for

inclusion in its Exemplary Science MonographSeries. Her chapter “Teaching Science WithStudent Thinking in Mind” will appear in a vol-ume to be released this fall. Dr. GrennonBrooks was also recently recognized by theAmerican Educational Research Journal for out-standing service in publications.

Dr. Grennon Brooks joined Hofstra’sDepartment of Curriculum and Teaching in2003. Previously, she directed the secondaryscience teacher preparation program at StonyBrook University, where she was the foundingdirector of both the Biotechnology TeachingLaboratory, a learning center for students andthe general public on emergent research tech-niques and issues, and Discover Lab, a clinicalpractice site for pre-service and in-serviceteachers. Dr. Grennon Brooks has held manyother positions in the field of education, includ-ing middle school science and math teacher,alternative education teacher for at-risk stu-dents, coordinator of gifted programs, andguidance counselor.

contexts (Sagor, 1990). These noviceteachers’ settings include diverse learn-ers, diverse subject areas and diverselearning environments. The broad aim oftheir action research studies is to facili-tate discovery and understanding oflearning processes while promotingteaching and learning based on thosenewly derived understandings. Patternrecognition is emerging as an area ofinterest on the national research horizon,and we are offering our Hofstra studentsthe perspectives, skills and tools neededto understand this dynamic way to thinkabout teaching and learning, and toimplement research-based pedagogy asprofessionals in the field.

References

ARC Center Tri-State Student AchievementStudy. (2000- 2001). Lexington, MA: The Consortium for Mathematics and Its Applications.

Bransford, J.D., Brown, A.L., and Cocking,R.R. (Eds.). (2000). How people learn: Brain,mind, experience and school. Washington,D.C.: National Academy Press.

Baker, L., and Brown, A. L. (1984).Metacognitive skills and reading. In P. D.Pearson, M. Kamil, R. Barr, and P.Mosenthal (Eds.), Handbook of readingresearch (pp. 353-394). New York:Longman.

Franklin-Leach, L.S. (1992). Hands-on sciencecurriculum helps female pupils. Researchstudy. Lubbock, TX: Texas Tech.

Hawkins, D. (1992). Investigative arts: Scienceand teaching. An opening chairman’saddress to the Second InternationalConference on the History and Philosophyof Science and Science Teaching held atKingston, Ontario, Canada.

Hyerle, D. (1996). Visual tools for constructingknowledge. Alexandria, VA: ASCD.

Hyerle, D. (2004). Student successes withThinking MapsTM. San Francisco: Corwin.

Jones, B. (1990). A developmental perspectiveof the child’s concept of sound: FOSS physicsof sound module. Master’s project,University of California at Berkeley,

NSF’s Engineering Research Centers,http://www.eng.nsf.gov/eec/erc.htm.

Klentschy, M., Garrison, L., and Amaral, O.M.(2001). Valle Imperial project in science:Four year comparison of student achievementdata 1995-1999. Research report, NationalScience Foundation Grant # ESI-9731274.

NAEP: National Assessment of EducationalProgress. (1999). Long term trend assess-ment. National Center for EducationStatistics, Institute of Education Science,U.S. Department of Education.Washington, D.C.

Sagor, R. (2000). Guiding school improvementwith action research. Alexandria, VA: ASCD.

Schoenfeld, A. (1988). When good teachingleads to bad results: The disasters of a“well taught” mathematics course.Educational Psychologist 23(2):145-166.

Stokes, D. E. (1997). Pasteur’s quadrant: Basicscience and technological innovation.Washington, D.C.: Brookings Institute Press.

TIMSS: Trends in International Mathematicsand Science Study. (1995, 1998, 2003).National Center for Education Statistics,Institute of Education Science, U.S.Department of Education. Washington, D.C.

HOFSTRAHORIZONS18