Details and purchase

Scientific Research

An exper­i­men­tal study on The Expert Math­e­mati­cian is reviewed on the US Depart­ment of Education’s “What Works Clear­ing­house” website…

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Teacher’s Advantage

Essen­tial fea­tures of effec­tive media. Effec­tive instruc­tion­al media must offer approved sub­ject mat­ter con­tent, appro­pri­ate­ly sequenced…

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Why Logo?

Lessons guide, stu­dents “dri­ve;” teach­ers help them nav­i­gate and under­stand. Logo is a dynam­ic log­ic tool that pro­motes focused, intentional…

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What is The Expert Mathematician™?

The Expert Math­e­mati­cian (TEM) Instruc­tion­al Sys­tem is an inno­v­a­tive tech­nol­o­gy-medi­at­ed mid­dle school math­e­mat­ics cur­ricu­lum. TEM sug­gests a pleas­ant irony—that learn­ing math­e­mat­ics inte­grat­ed with a pow­er­ful pro­gram­ming tool is actu­al­ly eas­i­er and more engag­ing because it gives stu­dents excel­lent con­trol of the math­e­mat­i­cal log­ic. Fur­ther, informed by evi­dence based instruc­tion­al design research, TEM pro­vides a strong ped­a­gog­i­cal frame­work for devel­op­ing the mid­dle school math­e­mat­ics cur­ricu­lum, mak­ing excel­lent use of com­put­er tech­nol­o­gy in Stan­dards-based math­e­mat­ics instruc­tion. TEM is cus­tom designed to max­i­mize stu­dents’ invest­ment in study­ing math while opti­miz­ing peer learn­ing, and sup­port­ing facil­i­ta­tive teach­ing. Instruc­tion­al mate­ri­als pro­vide 2 or more years of gen­er­al math­e­mat­ics, pre­al­ge­bra and alge­bra I con­cep­tu­al and com­pu­ta­tion­al con­tent. Research shows that TEM lessons can engage stu­dents and increase achieve­ment for main­stream and at-risk stu­dents, as well as increase pos­i­tive atti­tudes about learn­ing mathematics.

Uses of TEM include:

  • Stand-alone math­e­mat­ics foun­da­tion build­ing cur­ricu­lum for at-risk students.
  • Core dynam­ic math­e­mat­ics frame­work for con­struc­tivist prob­lem-based math­e­mat­ics program.
  • Can be used as tech­nol­o­gy-math com­ple­ment to direct instruc­tion curriculum.
  • After school tutorial.
  • Stim­u­lat­ing inter­ven­tion for high poten­tial ele­men­tary school students.
  • Excel­lent intro­duc­tion to real “key­stroke” com­put­er pro­gram­ming with mathematics.

Objec­tives of The Expert Math­e­mati­cian include:

EngageImprovePro­videMath­e­ma­tize
Engage stu­dents whether or not they’ve been pre­vi­ous­ly suc­cess­ful in math in an affec­tive­ly pos­i­tive and suc­cess­ful expe­ri­ence with math­e­mat­ics at this cru­cial tran­si­tion­al time pri­or to high school.

  • fill in gaps in con­cepts and skills
  • gain con­fi­dence in math­e­mat­i­cal prob­lem solving

Improve stu­den­t’s crit­i­cal think­ing, prob­lem solv­ing and team col­lab­o­ra­tion skills. Part of instruc­tion is to ensure that stu­dents under­stand how their class­room prac­tice pro­vides excel­lent rehearsal for work­place activities.

  • dis­cus­sion guide­lines empha­size spe­cif­ic skills sup­port­ed by research evi­dence show­ing pos­i­tive out­comes and work­place expectations.

Pro­vide an engag­ing and sound intro­duc­tion to com­put­er pro­gram­ming with math­e­mat­i­cal tech­nol­o­gy as experts use it in real work.

Yes? Logo devel­op­ers often tout­ed the capac­i­ty of Logo to instill in stu­dents an innate/intuitive under­stand­ing of mathematics—gleaned from work­ing with the “tur­tle” object that visu­al­ly depicts math­e­mat­i­cal expres­sions. To some degree that claim seems valid. How can this vital Math-sense be fur­ther instilled? Use the math­e­mat­i­cal attrib­ut­es of the class­room as con­crete exam­ples of math facts. Fol­low­ing are a few exam­ples:

  • Area: floor, walls, ceil­ing (walls = area walls — area win­dows) Can be depict­ed as a Logo exer­cise. If tile floor­ing has insets, set up expres­sion on paper (graph paper if time allows) to dis­tin­guish: Area of insets + area with­out insets-= total area; then imple­ment in Logo. Ceil­ing tiles can also be depict­ed: To define area, minus space occu­pied by light fix­tures. Ceil­ing area minus light fix­tures (= x), plus area cov­ered in light fix­tures (= y). Then x + y = total ceil­ing area.

  • Perime­ter of learn­ing space. Stu­dents cre­ate plac­ards to des­ig­nate and walk around perimeter.

  • Frac­tions, per­cents: ceil­ing, tile floor with insets.

  • Pythagore­an the­o­rem: stu­dents walk 4 sides of a square perime­ter, count­ing their steps toe-to-heel (record­ing the num­ber); then cut across on the diag­o­nal, count­ing their steps (record­ing the num­ber). Data is then entered in a Logo pro­ce­dure to deter­mine math­e­mat­i­cal­ly cor­rect angles and ratio to cre­ate and save “square-diag­o­nal” procedure.

If stu­dents are stum­bling in oth­er con­struc­tions, they can be coaxed (light-heart­ed­ly) to stand, point for­ward, walk a few steps and turn (etc.) to inter­nal­ly sense how the Logo tur­tle must move to depict a math­e­mat­i­cal expres­sion to rep­re­sent the hypotenuse—thus feed­ing back to the terms of the expression.

The third objective—Provide—also helps meet a num­ber of edu­ca­tion­al tech­nol­o­gy stan­dards for stu­dents and teach­ers as sug­gest­ed by ISTE, 2017. Teach­ers will see these goals come to life while con­duct­ing our hands-on instruc­tion­al format.

A bonus fea­ture of TEM’s coop­er­a­tive­ly struc­tured pre­scrip­tive-gen­er­a­tiveTM media is the insights it intro­duces regard­ing cog­ni­tive and social process­es cru­cial to learn­ing inde­pen­dent­ly and in peer col­lab­o­ra­tion. Increas­es on stan­dard­ized tests can be expect­ed. This is far more than a skill-drill pro­gram. TEM is a devel­op­men­tal learn­ing sys­tem that hon­ors stu­dents’ needs for a com­pre­hen­sive expe­ri­ence gen­er­at­ing, edit­ing, oper­at­ing, anno­tat­ing, dis­cussing real math­e­mat­i­cal prod­ucts that are stu­dent-built on a dai­ly basis using a com­put­er, and learn­ing coop­er­a­tive­ly with peers.

The Expert Math­e­mati­cian Instruc­tion­al Sys­tem is an eco­nom­i­cal pro­gram, cus­tomized to give teach­ers and stu­dents unusu­al lever­age in over­com­ing bar­ri­ers to learn­ing math­e­mat­ics. It can enhance any mid­dle school math­e­mat­ics cur­ricu­lum. See oth­er links.

TEM intro­duces a learn­er-cen­tered, dynam­ic gen­er­a­tive learn­ing mod­el to the mid­dle school math­e­mat­ics cur­ricu­lum. 196 40–120 minute con­struc­tivist lessons include hun­dreds of inter­ac­tive com­put­er-medi­at­ed prob­lem solv­ing exer­cis­es that teach math­e­mat­i­cal con­cepts and devel­op com­pu­ta­tion­al skills. Stu­dents of diverse abil­i­ty lev­els and learn­ing styles have con­sis­tent­ly shown their inter­est in the TEM pro­gram, and have achieved.

All con­struc­tivist pro­grams have at least one com­mon fea­ture: in vary­ing mea­sures they shift author­i­ty and respon­si­bil­i­ty for con­struct­ing new knowl­edge to the stu­dent. There are cog­ni­tive and affec­tive learn­ing ben­e­fits from this shift–if the media sup­ports it. Cog­ni­tive­ly, stu­dents are able to hold instruc­tion­al con­tent in short-term mem­o­ry longer when they direct­ly con­trol media. This is cru­cial to fit­ting togeth­er and build­ing links between new infor­ma­tion and pri­or knowl­edge. Teacher-direct­ed pac­ing, on the oth­er hand, can frus­trate stu­dents’ abil­i­ty to linger with a con­cept long enough to grasp it. While core sub­ject mat­ter is pre­scribed, TEM is designed to give stu­dents need­ed con­trol over work­ing with new concepts.

Copy­right James Bak­er, 2020, 2021. All rights reserved. No por­tion of this page may be copied or dis­trib­uted with­out express writ­ten per­mis­sion of the author.