a discourse on conceptual understanding and best practices

8/19/2019 A Discourse on Conceptual Understanding and Best Practices

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A DISCOURSE ON

CONCEPTUAL

UNDERSTANDING AND

BEST PRACTICES

By: K. Beckford-Thomas



THANK YOU

The future of mankind lies not inthe hands of new technologicalinventions and scienticbreakthroughs. It lies in thehands of ambitious teachers likeyou… because that’s where it all

starts from. Thank you.



OUTSIDE THE BOX

“Students must learnMathematics with

understanding, activelyuilding new knowledge

from e!"erience and "riorknowledge#.

$%&$'($)*$• &ast &resent +uture



TO TEACH IS TO CONNECT sing real worldlife e!"eriences which use

Mathematical "rinci"les.

(nfuse life into the content y awakening

students own imagination.

Tunnel vision is

$%T()*T



MATHEMATICAL

PROFICIENCY

“/s for the student,

mathematical "roficiency is

for the teacher, of

"aramount im"ortance#.



SIGNS OF MATHEMATICAL

PROFICIENCE

The art of teachi! i"# the art of $eari!%

*once"tual

understanding

&rocedural fluency

Strategic com"etence

/da"tive reasoning

&roductive dis"osition



$0$' 1$/')()2:

Teachers are first students. (f you cant allow yourself to e taught,

you shouldnt e a teacher.

“There are few things more "athetic than those who have lost their

curiosity and sense of adventure, and who no longer care to learn.#

4 Gor&o B% Hic'$e(,

“Those "eo"le who develo" the aility to continuously

ac5uire new and etter forms of knowledge that they can

a""ly to their work and to their lives will e the movers

and shakers in our society for the indefinite future.#

4 Bria Trac(

http://www.goodreads.com/author/show/313356.Gordon_B_Hinckley

http://www.goodreads.com/author/show/22033.Brian_Tracy

http://www.goodreads.com/author/show/22033.Brian_Tracy

http://www.goodreads.com/author/show/313356.Gordon_B_Hinckley



The Millennials:

To learn or not to learn, thats the 5uestion.

6.The generation is generally disinterested in leaning.

7. 8e are fighting a losing attle.

9. The use of technology as a classroom teaching tool is

overated.

. My students "erformance in Math lies s5uarely at my

feet.



THE EFFECTI)E TEACHER Begin a lesson with a short review of "revious learning.

Begin your lessons y sharing the lesson o;ectives.

&resent new material in small ste"s, "roviding for student

"ractice after each ste".

2ive clear and detailed instructions and e!"lanations.&rovide a high level of active "ractice for all students,

regardless of varying levels of intellectual ca"acity.

/sk a large numer of 5uestions, check for student

understanding, and otain res"onses from all students.

2uide students during initial "ractice.

&rovide systematic feedack and corrections.

&rovide e!"licit instruction and "ractice for seatwork

e!ercises and monitor students. <This cannot e over-

em"hasi=ed>



BEST PRACTICES



THE GOAL FOR *HICH *E

STRI)E Tirelessly we toil. ?ays and nights of

unending "re"arations for that one day@

when fate meets our students and *S$* Math

e!am ecomes that rick wall that must econ5uered to reach the other side. That

sweet victory of grade (, finally its here and

we are done.

Aet not without the scrutiny that meetsevery 5uestion.



TOPIC BY TOPIC ASSESSMENT

*S$* Structured uestions

6. *om"utation

&erformance: satisfactorymean mark: C.76 out of 67

&rolem areas: Dire &urchase, ratio E &ro"ortion.

Solution:Take a real life a""roach when teachingcom"utation es". consumer math. Sell the

calculator as students friend. /ssign mini "ro;ects

which uild students understanding of conce"ts.



ALGEBRA &erformance: satisfactory

Mean Mark: F.GH out of 67

&rolem /reas: ?irected )umers, writing ofe5uations from statements, trans"ostion,

simultaneous e5uation<elimination method>

Solution:?istriutive "ro"erty must e taught

rigorously. Stress the diff. etween e!"ressions

and e5uations.



SETS + CONSTRUCTION &erformance: unsatisfactory

mean mark: F.H out of 67

&rolem areas: /&&1(*/T(I) I+ *I)T$)T

/gain real life a""lication used in set teaching.

Set language must not only e taught ut used

regularly.



MAPS + SCALE DRA*ING

'ed +lag area: unsatisfactory

Solution: (ntegration across su;ect areas

$g. 2eogra"hy.

1et the students use their immediate

surroundings to hel" in understanding of area.

$g. se a ma" of the school etc.



TRANSFORMATION +

TRIGONOMETRY nsatisfactory

Transformational language should e taught

rigorously from the lower levels.

'atios E 'ules: Teach conce"ts se"arately and

cautiously. Students are a""lying rules where

ratios are necessary and vice versa.



RELATIONS, FUNCTIONS AND

GRAPHS nsatisfactory

*once"t of tangent to a curve is foreign to

most students. The "ro"erties associated with

"arallel and "er"endicular lines not wellrehearsed.



STATISTICS + PROBABILITY Satisfactory

Measures of central tendency as key conce"ts.

*lassroom activities a must. 'eal lifea""lications cannot e divorced from this

to"ic.



NUMBER PATTERNS Moderately well

se the conce"ts of se5uences and series in

otaining rules for a "articular "attern.



GENERAL AD)ICE IN

CONCEPTUAL UNDERSTANDING Know the content almost too well

Teach with confidence

Save on time y team teaching

se your colleagues as resource

Technology is your friend ?evelo" a keen eye for students differences in learning styles

and "ersonality. This "lays a key role in their ultimate

"erformance.

)ever assume they know or have "rere5uisite knowledge.

'eca" and regurgitate.

Be as sim"le and "ractical as "ossile. /t any level, teach

sim"ly, teach "ur"osefully, teach humly.

B$ AI' ST?$)TS +('ST SI'*$ I+ ()+I'M/T(I). This

involves eing accessile, "atient, tolerant and friendly<yet

not familiar>



THE END

a discourse on conceptual understanding and best practices

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