HCESC Tech Academy August 8, 2013
Talk by Fred Annexstein, University of Cincinnati
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The next ten years present an important turning
point in mathematics and technology K12 education. Will computers be an
integral part of standard K12 education? Will computer science be an
essential and mandatory part of every high school curriculum? Will high
school mathematics curricula be refactored to take advantage of the
calculation and visualization powers afforded by modern tablet computers?
The technological world has changed dramatically
in the last 20 years. However, as a professor of computer science at the
University of Cincinnati, I have seen little change in the skill set of
incoming freshman. Math and quantitative literacy are certainly among the
most important skills that new students bring to their higher education
institutions. However, when reviewing standard middle and high school mathematics
textbooks, I see a disconnection from my world-view as a working professional
in mathematics.
All our futures are now tied to the advances in
computing, and the math, logic, and software that defines computation.
Therefore, much is to be gained by addressing the role of computers and math in
K12 curriculum directly. Articulating the design of a mandatory curriculum that
integrates math, digital literacy and computer science, can and will have a
positive impact on individual students, and have a significant impact on society
as a whole.
First, there is the economic impact associated with having a better technically
trained and scientifically educated student body. The demand for tech skills
in the modern workplace is well documented. (A sense of the scale of the
demand is reflected in the fact that there are currently 3000 unfilled IT and
Computing jobs in the Greater Cincinnati area.) Second, there is the intellectual impact associated with
understanding the scientific significance of computers, statistics, and
information theory, which is accessible to every high school student. Third,
there is the emotional impact
associated with the feelings of freedom and the joys of discovery that can
emerge from young people through interaction with and control over technology.
Fourth, there is the cultural impact
associated with a tech knowledgeable and civically engaged citizenry. There
is no doubt that to understand and engage with issues of cybersecurity and NSA
surveillance, for example, one needs to know how computing system such as
PRISM and XKEYSCORE work, and this requires a basic understanding of
computers and their design.
On the other side of the fence are those who
prefer to avoid going down the route to integrate computers and computer
science into standard K12 curriculum. One argument on this side is that for
most careers domain knowledge is more important than computer coding skills,
and most people will not be coding directly, even if students will likely be
using modern computers in the workplace of the future. Another set of arguments against
integrating technology in schools has the effect of “ghettoizing” computer
coders into an elite class of mathey nerds, often with a prejudice that coder
culture is exclusive, puerile, and male.
Deep
Digital Literacy
To achieve any level of depth in digital literacy,
students must be able to learn and produce computer code. This digital
literacy extends into quantitative, math and science literacy and has the
potential to bring the curriculum of those subject areas up to date and
present them in a context that would be more recognizable to a modern working
professional.
Concepts
of the Internet
To deeply understand the Internet and the World
Wide Web a student needs some coding skills. The Internet is coding “all the
way down”, from front-end technologies such as HTML, Javascript, CSS, to the
back-end technologies such as SQL, Linux, Windows; from the specs and
protocols running the worlds networks such as HTTP, TCP, FTP, to the mobile
applications running the modern economy such as Android, iOS, Gmail, Twitter
and Facebook, and the scripts and programming frameworks that glue it all up
together such as Ruby, Python, Java, C++, Perl, ObjC. Of course, a student could only learn a
small fraction of details of the coding architecture of the web, however
understanding its overall design and underlying principles are within the
grasp of every student.
Concepts
of Physical Simulation
Physics and engineering in the real world is
understood through numerical simulations performed by computers. This is the
real math, and why math is important, and how math gets done. High school
math curriculum that focuses on hand-calculations at the expense of avoiding a
focus on this real-world math is doing students and society a disservice.
Concepts
of Information Science
The digital age begins with the theory of
information science created by the pioneering work of people such as Alan Turing
and Claude Shannon in the 1930s and 1940s. The concept of the algorithm, the
universal machine, entropy, encoding and decoding information—this is the foundational
science part of the digital age. Turing’s breakthrough idea was that computer code is universal, that is to say, anything that is possible to compute
is possible to compute with a very simple machine and an algorithmic idea
expressed in a form appropriate for that machine. Turing’s genius is still underappreciated
today. James Gleick’s book “The
Information: A History, a Theory, a Flood” presents this new science of
information through engaging biographies, such as those of Turing and
Shannon.
A
visionary who took early note of the power of computers in science and math education
was Seymour Papert. Professor Papert
is credited with an influential theory on learning called constructionism, and he states, “The role of the
teacher is to create the conditions for invention rather than provide
ready-made knowledge.” In his seminal book “Mindstorms: Children, Computers, and Powerful Ideas” (1980) he speaks on the
revolutionary impact of project-based student work using computers.
The Problem with Algebra
“Is
Algebra Necessary?” is the title of a provocative NY Times opinion piece by
Andrew Hacker that was published July 28, 2012, and has provoked over 500
comments and many blogs. Hacker argues that when legislators require that “every
young person should be made to master polynomial functions and parametric
equations”, then they are missing the point of quantitative literacy. Educators are trying to respond to a looming crisis in
which there are math education mandates and widespread dislike by students
and other stakeholders for the current state of curricular affairs. A number
of educators have suggested that introducing computers can address some of
these issues, but in most states computer science is an elective that does
not satisfy any math requirements. The quantitative literacy of American
students is under scrutiny, and traditional algebra courses do not seem to
add up.
To get a
sense of the disconnect in K12 math affairs, let us consider a well regarded
textbook and curriculum provided by SaxonMath, published by Houghton Mifflin
Harcourt. The principles underlying the design of SaxonMath are that it
provides “Consistent Lesson Structure” and “Distributed Units of Instruction.”
The motivation being that a consistent structure provides teachers with a
“predictable routine” in the classroom, and the distributed practice claims
to “provide students with depth of
understanding”. The curriculum is divided into many dozens of micro-lessons
with topics changing on a daily basis. Topics are shuffled in and out through
the year.
For
example, here is a selection of three contiguous micro-lessons from Saxon
Algebra 1, which would probably be covered in one week in an 8th
grade classroom setting:
*Lesson
12 – Using real numbers to simplify expressions
*Lesson
13 – Calculating and Comparing Square Roots
*Lesson
14 – Determining the Theoretical Probability of an Event
The
textbook continues in this way covering over 120 micro-lessons.
Each of
these micro-lesson topics is, of course, on its surface very important to
mathematics education. But where do we see any “Big Ideas?” How do all these shuffled
lessons fit together into a coherent picture of mathematics? And how do students
react to the material? Do students reflect on the material beyond the fact
that “math is too hard for me,” or “math is an easy A!”? We should desire and
celebrate situations where a student says, “Hey, I can do that problem easier on a calculator
or computer.” Recognizing when a problem is in a form ready for calculation
by code reflects depth of understanding. A student who understands some simple
ideas of computer math, e.g., a
computer algorithm to calculate square roots and code that can estimate
theoretical probabilities would be far better equipped for today’s world.
A
recommended online resource is a TedTalk entitled “Stop Teaching Calculating,
Start Teaching Math” by Conrad Wolfram in which he advocates for a new math
curriculum based on using computers for calculation (see website http://computerbasedmath.org ). Wolfram indicates that math is
a four step process: 1) posing the problem, 2) formulating in mathematical
language, 3) calculation/computation, and 4) verification. He suggests that
currently 80% of student time is spent in doing step 3 using hand
calculations, whereas ideally computers should be used to free students to
devote more time to other steps. Students can achieve greater depth of
understanding when curriculum is directed at formulating and modeling
problems mathematically. Recently, efforts in this direction have been adopted
by some European nations, thus far focusing on statistics curriculum in high
schools, with potential to expand to other math grades.
A Project-Based Curriculum using
Computers and Coding
High
school students must become familiar and comfortable using computers as
calculation engines. At the start of such an endeavor, there are great
benefits to giving students an artistic
experience with technology. Such experiences can strengthen students,
giving them self confidence, and can work against the more harmful effects of
technology in the modern age. One
curriculum idea that I have worked with in the setting of an 8th Grade
classroom is to use modern software on laptops that provide a platform for students
to become “Algorists.” An algorist, or algorithm artist, is someone who uses
computer coding to generate artistic media, images, sounds, etc. Much more
than cut and paste is expected here, and students really create their own art
works. This fits the need for middle schoolers to experience self-reliance
and supports their inclination to create their own media. There are several actively
supported computing platform tools to help students achieve this goal. There
are very good Java
and Python media computing textbooks that support introduction of computer
science concepts, such as Barbara Ericsson’s and Mark Guzdial’s (Georgia Tech)
An Introduction to Computing and Programming with Java: A Multimedia
Approach (2006).
Computer gaming is an excellent way to both
engage students and to introduce physical simulation. The mathematical
modeling of gravity, the science of falling and projected bodies, and the
algebra of force vectors are all well motivated in computer games and
animations. There are several low-overhead entry points for students and
teachers to begin working on computer physical simulations.
Scratch/TurtleArt – TurtleArt and Scratch are applet
based art-programming environments, Both can be used by young students to generating
images using turtle commands, such as move, turn, and pen down. Scratch has
been designed with “wide walls” allowing the popular platform to be used for
many purposes. In these friendly environments, students program by snapping colorful
code fragments together like Lego building blocks. Scratch is excellent choice
to use to support digital literacy, digital design, and when introducing
basic computing concepts like variables and flow of control (see, http://scratched.media.mit.edu/ )
Linux/Python/Perl – It is relatively easy, using
these technologies, to set up a command line (non proprietary) environment
that gives students more control over the processing power of the computer.
Python and Perl are languages that can be used to provide an important functional
programming environment, one that is used successfully by students to do
powerful text and media processing.
Processing - Processing is a programming language designed to promote software
literacy within the visual arts and visual literacy within technology.
Initially created to serve as a software sketchbook and to teach computer
programming fundamentals within a visual context, it is now very mature software
and exciting for more advanced students.
Here are some final thoughts: Technology moves very rapidly, and computer languages and platforms come and go with increasing frequency. Teachers must give up on being gatekeepers to tech knowledge and focus efforts on mentoring in a tech culture. The focus of education should be on creating environments where students care really “see” math in action and building school cultures where self-assured students armed with computer lab or simple tablet and an ability to code can meet important challenges of science and technology straight on.
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Handout for talk on
“Everybody’s Coding”
Mathematics/Computer
Science/Technology - Resources for K12 Education
By Fred Annexstein,
University of Cincinnati, fred.annexstein@uc.edu
“The context of human
development is always a culture, never an isolated technology." -
Seymour Papert, mathematician, computer
scientist, educator, founder of MIT Media Lab.
Inspiring TED Talks:
*Mitch Resnick: Let's teach kids to
code: http://youtu.be/Ok6LbV6bqaE
*Conrad Wolfram: Teaching kids real
math with computers: http://youtu.be/60OVlfAUPJg
Supporting Websites:
*Computer Science Teachers
Association: http://csta.acm.org
*Computing at School (UK): http://www.computingatschool.org.uk/
*Code.org: http://code.org
*Mark Guzdial’s Computing Education
Blog: http://computinged.wordpress.com
Curriculum Resources:
*ACM K12 Model Curriculum: http://csta.acm.org/Curriculum/sub/CurrResources.html
*UK K12 Computing Curriculum:
Supporting Platforms
and Tools:
*Scratch / TurtleArt
“visual programming using legos” http://scratched.media.mit.edu/
*Processing “software literacy within the visual arts “ http://www.processing.org/
*Alice “OO programming in 3D environment” http://www.alice.org/
*Code Academy “learning in
web-based javascript environment” http://www.codecademy.com/
*Linux Environment for Education: http://www.edubuntu.org/
*Microsoft Dreamspark “MS
software for students and educators”
