From Pencil to Computer in Math Education

JUAN JOSÉ PRIETO-VALDÉS

(PART-I, from IV)

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 2

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 3

Computation: New kind of science

When calculators and computers initially became available to schools there was much optimism about their use in mathematics teaching. However, the reality was different, as facilitating calculation became the Achilles heel in further understanding of mathematics, resulting that math education has slipped backward. http://www.youtube.com/watch?v=60P7717-XOQ

Stephen Wolfram

What about Mathematics?

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 4

Many educationalists have discussed the problem arriving to the conception:

In many cases, the technology was used to search for a quick and easy solution, but not to deepen the understanding of the

concepts.

“stop teaching calculating and start teaching Math” (1)

http://www.youtube.com/watch?feature=endscreen&v=60OVlfAUPJg&NR=1

http://www.google.com/#hl=en&sugexp=les%3B&gs_rn=3&gs_ri=psy-ab&gs_mss=%22arriving%20to%20the%20%20conception%22%20&pq=arriving%20to%20the%20new%20conception&cp=16&gs_id=4g&xhr=t&q=%22arriving+to+the+conception%22&es_nrs=true&pf=p&tbo=d&sclient=psy-ab&oq=%22arriving+to+the+conception%22+&gs_l=&pbx=1&bav=on.2,or.r_gc.r_pw.r_qf.&fp=419282b094d9367&biw=1794&bih=989&bs=1

Conrad Wolfram

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 5

Computation = New Conception

math ≠ calculatingmath >>> calculating

Correctly using computers is the silver bullet for making math

education workStephen & Conrad Wolfram

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 6

Different Points of View

• METHOD – A: some authors consider that traditional pencil-paper method is the most appropriate.

• METHOD – B: others support the idea of using computers, as the best way to improve learning of mathematics and related science disciplines.

Correctly using computers

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How to use your computer correctly?

Teaching programing languages, etc… 

  \[ \int_0^R \frac{2x\,dx}{1+x^2} = \log(1+R^2).\]

  

  

\[ \lim_{x \to +\infty} \frac{3x^2 +7x^3}{x^2 +5x^4} = 3.\]

…From Pencil to Computer in Mat Education, J.J. Prieto-Valdes

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 8

Different Points of View

• METHOD – A: some authors consider that traditional pencil-paper method is the most appropriate.

• METHOD – B: others support the idea of using computers, as the best way to improve learning of mathematics and related science disciplines.

Combined method

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes 9

The present work reports

An innovative instructional technique created on the basis of mixed methodology (Pencil-Computer) comprising:

(1)electronic pen,

(2)handwritten recognition program, and

(3)processing software capable to solve and graph equations among other applications and interactions with the user.

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1. Method and system for digital pen assembly, US PAT EP 1861771 B1. Digital pen comprising: an electric circuit; an acoustic transmitter, detached from said electric circuit, and configured to transmit acoustic signals, said acoustic transmitter (100) being an ultrasound transducer and said acoustic signals being…

2. Digital pen and paper, US Pat 7,542,607. Digital pen and paper system comprising a pen arranged to make pen strokes on a document having a plurality of regions, to detect markings on the document, and to record them in a series of samples, wherein: the system is arranged to determine from the samples the position of the pen strokes; the system has defined therein a plurality of different warning conditions that determine when a warning will be produced in response to lost samples…

3. Electronic pen and method for recording of handwritten information, US Pat 7,385,595 . System for electronic recording of handwritten or hand-drawn information, comprising: an electronic pen which is intended to be moved in desired pen movements across at least one base and to register the pen movements as a plurality of digital pen strokes; and a processing device for receiving registered digital pen strokes from the electronic pen, the digital pen strokes including a first type, which is processed by the processing device as graphical information constituting said information to be recorded, and a second type …

From Pencil to Computer in Mat Education, J.J. Prieto-Valdes