Addi­tion­al infor­ma­tion is con­tained in the main site page and the down­load­able, Guide­lines to Teach­ing TEM document—both accessed by log­ging in, below.

The math­e­mat­ics micro­cul­ture. Learn­ing the tools and terms and prac­tices of the microculture.

The Expert Math­e­mati­cian pro­gram was devel­oped as an aca­d­e­m­ic chal­lenge inter­ven­tion that inte­grates a set of rel­e­vant and well-estab­lished the­o­ries of learn­ing and teach­ing, with cus­tomized les­son media, that com­bine to increase oppor­tu­ni­ties for both teach­ers and stu­dents to achieve improved out­comes. Con­duct­ed as designed, TEM enhances authen­tic con­fi­dence of stu­dents and teach­ers,  trans­lat­ing to moti­va­tion, engage­ment and learning.

Stu­dents with 6th grade read­ing skills should be able to under­stand les­son instruc­tions. One impor­tant advan­tage of stu­dent-cen­tered learn­ing is that stu­dents have some con­trol of les­son pac­ing. This fea­ture enables the learn­er to pause as need­ed to grasp a con­cept, before dash­ing on—an added ben­e­fit in deci­pher­ing tech­ni­cal lit­er­a­ture. Respect­ing this need of dis­ad­van­taged stu­dents is important—not to let them drift off too long, but acknowl­edg­ing that many of these stu­dents have nev­er under­stood some log­i­cal or seman­tic terms that a teacher might take for grant­ed. So stu­dents seem­ing “adrift” may sim­ply need more time to process a les­son ele­ment in terms of their exist­ing knowl­edge. They should be encour­aged to “give it your best think­ing,” but also know that the teacher will be around to help with a need­ed clarification.

Work­ing with a peer and with Logo and per­haps a lit­tle coach­ing, they can fill them in.

Prepar­ing to con­duct class. Teach­ers must active­ly work through lessons before assign­ing them to stu­dents. Les­son prepa­ra­tion is impor­tant for two reasons:

1. Aware­ness of les­son con­tent and objec­tives, so any con­fu­sion can be con­fi­dent­ly facil­i­tat­ed to clarity.
2. Readi­ness to raise inter­est­ing ques­tions relat­ed to the les­son content—such as, “if you change this con­stant (or vari­able input), what is the math­e­mat­i­cal result?” Then (gen­tly prob­ing, while expect­ing to coach or nudge with a hint), “Can you see why you got that result?” Fol­low­ing up with a brief inter­ven­tion, draw­ing from rehearsed Big Ideas in math­e­mat­ics, can deep­en stu­dents’ under­stand­ing of a con­cept and—importantly—help them to make con­nec­tions between the present item of study and pri­or con­cepts. Big Ideas in math­e­mat­ics are fur­ther dis­cussed with sources in the main site page and the down­load­able Guide­lines for Teach­ing TEM, fol­low­ing sign-in below.

“This is all prob­lem-solv­ing”, one suc­cess­ful teacher of TEM, com­ment­ed. But it’s engag­ing and with teacher’s light­heart­ed sup­port and rein­force­ment of stu­dents’ use of col­lab­o­ra­tive skills (each stu­dent doing their part; and—if needed—use of reward tokens with week­ly draw­ing for small prizes), stu­dents will increas­ing­ly make the effort and they will learn. Using Logo has its own rewards: as not­ed, stu­dents can feel math­e­mat­i­cal­ly com­pe­tent like they nev­er have previously.

Sched­ul­ing class­es: Peri­od or block? Orga­ni­za­tion­al­ly, there’s a lot going on in The Expert Math­e­mati­cian learn­ing com­mu­ni­ty. Stu­dents need enough time to pick up their mate­ri­als, get set­tled, and begin work. Time should be allot­ted for stu­dents to write out, work, and turn in a cou­ple of cal­cu­la­tion prob­lems before start­ing on the day’s les­son. To estab­lish momen­tum, allow­ing stu­dents enough time to active­ly engage their les­son is impor­tant. A sin­gle 45–50 minute class peri­od is scarce­ly enough time for thought­ful engage­ment and teacher sup­port. Nine­ty minute block sched­ul­ing is strong­ly encouraged.

Back­ground the­o­ries at work. Ped­a­gogy, the­o­ry, social-cul­tur­al tools ZPD and “tools” should be lead­ing facil­i­ta­tive process (con­trast with con­tent) Fine-tun­ing the col­lab­o­ra­tive peer inter­de­pen­dence part will car­ry the chal­leng­ing days. Gen­tle reminders that, “we are in this togeth­er; we help each oth­er suc­ceed” (cou­pled with check­list rein­force­ment) will be reas­sur­ing. And, you will see Vygot­sky’s social-cog­ni­tive the­o­ry in prac­tice. Many stu­dents under­stand this (intu­itive­ly) from a team sport; that’s one micro­cul­ture. Now they are prac­tic­ing bring­ing these skills into the cul­ture of math­e­mat­i­cal prac­tice that will be use­ful in the world of work.

Of dis­ad­van­taged stu­dents you are ask­ing a lot, so it’s impor­tant to be direc­tive in get­ting set up and start­ing lessons, but then light­heart­ed and patient in cul­ti­vat­ing peer work habits and the “growth mind­set” as stu­dents process math­e­mat­i­cal ideas.

Teach­ers also check in briefly with stu­dents to deter­mine their com­pre­hen­sion, facil­i­tat­ing stu­dents to cor­rect under­stand­ing of les­son points, as needed.

Cal­cu­la­tion skills. Stu­dents jump right into lessons. When rou­tines have been estab­lished, they begin to prac­tice com­pu­ta­tion­al skills. Stu­dents should have some choice in which skills to prac­tice, but they should try to keep their choic­es con­sis­tent with con­cept lessons. They should acti­vate and oper­ate a game, write out the prob­lem on a half sheet of paper and do the cal­cu­la­tion on paper to deduce the answer. The answer is then keyed in to check accu­ra­cy. Although stu­dents are work­ing togeth­er, they should each do two dif­fer­ent prob­lems and hand them in. Cal­cu­la­tion pro­fi­cien­cy is impor­tant but should not delay work­ing through the lessons to learn and apply con­cepts to solve prob­lems. This is a major strength of the pro­gram. If ses­sions are lim­it­ed to 40 min­utes, get­ting set­tled, pick­ing up their fold­er, get­ting start­ed need to hap­pen fast. Nine­ty minute block sched­ul­ing works better.

Fol­low­ing is a still-life cameo of stu­dents at work and teacher rein­forc­ing skills practice.