Standard
12 - Teacher leaders will evaluate and use technology for teaching and
learning.
Traditionally,
the mathematics classroom has been a space where teachers lecture and students
take notes followed with some practice. This is especially true of the
higher-level classes such as AP Statistics and AP Calculus. In my quest to
increase engagement and rigor, I decided to work to finding ideas of how I can
use technology to help my students' understanding and problem solving. I am not
interested in introducing technology for the sake of using technology. As,
Merzenich states that, "simply adding computers to conventional teaching
strategies is an unsophisticated approach that, it is not surprising, adds very
little to students' experiences in the classroom" (as cited in Robin,
2008, p. 221).
Beginning
the program, I decided to find out how to create genuine opportunities for
learning and investigation math. Whether that means using programs such as ST
Math or Think Through Math, both are adaptive to students' needs. Or, utilizing
free technology such as GeoGebra or Desmos to help students gain a different
perspective. An article by M. Hohenwarter, L. Hohenwarter, Kreis, and Lavicza,
suggested the use of GeoGebra in an upper level class such as calculus. This
was not an obvious connection, but Hohenwarter et al., found that this tool may
be used to "help students to better understand their algebraic
manipulations of functions, to visualize characteristics of certain types of
functions, and to improve their skills of sketching graphs of functions and
their derivatives" (2008, p. 4). Students can certainly learn about upper
level math the "traditional" way via lecture and practice, but may
reach greater depths of understanding working with the reasons why certain
properties and theorems work (effectively learning the why, not just the how).
Additionally,
my school district has added adaptive learning tools to interact with math in
different ways. One, ST Math, looks at math in a non-equation way
showing pictures and game-like activities to teach the basics associated with
Algebra, Geometry, and all pre-high school level classes. The other, Think Through Math,
looks at math in a more traditional way utilizing various feedback including
live tutors and immediate feedback. I have had the opportunity to utilize both
with various classes over the past several years and have found my use of them
with my classes to be less than successful. So, I decided to research how I can
best utilize either with my classes if I should choose to do so.
An
idea formed from reading an article by Arroyo, Woolf, Burelson, Muldner, Rai,
and Tai is to use journaling as a supplement to regular program use. I
believe that journaling is one way in which students can record their affective
traits and thoughts about what and how they are learning the material. An
additional supplement to the software could be regular information gathering
around via formative quizzes. One possible avenue for creating quizzes that
could help streamline the process for information gathering is a resource
like Quizlet.
I could use Quizlet or a similar technology to have students reply to questions
based around what they learned, how they learned it, what information they
required help on, and how they felt throughout the process of using the
program.
Throughout
the Teaching with Technology class, I wanted to discover what it means to be a
technologically innovative math educator. Research by Sherman (2014), I read
outlined two vital aspects of technology use that are necessary to deepen
students' mathematical knowledge. The first category used in the article is the
use of technology as an amplifier. The article states that the amplifier use,
"supports a shift in the focus of students’ mathematical activity and
thinking from drawing and measuring to looking for patterns and making and
testing conjectures” (2014, p. 223). I am currently using at least one
amplifier in my classes, the graphing calculator. This resource has allowed my
students, while working with transformations, to get past worrying about making
a table, and remembering rules to make a graph and allows them to get to the
inner workings of transformations. The second category used is the reorganizer.
The reorganizer "has the power to affect or shift the focus of students’
mathematical thinking or activity" (2014, p. 223). In reflecting on my
practice, I realize that I do several things associated with either the
amplifier or the reorganizer, but very few of them rely on technology right
now. To move toward being an innovative educator, I will need to work on
incorporating technology tools as a means of moving toward deeper learning.
Additional research by Starkey, offered some other
interesting points of reference in determining the efficacy of technology
including collaboration and connection to prior learning. These areas are very
important in being learners with technology as they allow students to process
the information gathered or learned. When students are collaborating, they can
process new learning together which gives students the potential for multiple
points of entry. These multiple points of entry are vital to putting their
learning into their own words and style of understanding. Similarly, connecting
their learning to other areas of knowledge, especially to previous knowledge,
allows students to deepen their understanding and connect different issues. Both
these aspects can help to strengthen any new learning and better student’s
problem solving abilities, both of which elevate their ability in math.
We
further learned about the legal ramifications of technology use in the
classroom and what to look out for as teachers. There are many laws surrounding
the expectation of privacy for students in public school systems, especially
regarding the use of technology. Unfortunately, these rights to privacy are not
always easy to enforce or ensure with the prevalence of technology use in
today's school environment. Research by the Center for Educational Privacy and Law at
the University of San Diego (CEPAL), revealed one of the most interesting
concerns for privacy that schools face is called householding.
"Householding allows data collection to occur across devices regardless of
whether or not they are owned by a district or owned privately by a
student" (CEPAL, 2015, p. 6). This rather sneaky method for data
collection is strong enough to pinpoint usage across devices at any time, so
students are not immune to data collection whether working on school work at
school or home. The many laws that protect student autonomy are not much of a
deterrent to this sort of activity. The Family Educational Rights and Privacy
Act (FERPA), Protection of Pupil Rights Amendment (PPRA), and Children's Online
Privacy Protection Act (COPPA), are limited in what they have jurisdiction over
and the depth to which online information is protected. For example, FERPA does
not have any consideration for third party application operators, the PPRA has
made considerations for protection, but does not include any currently, and
COPRA only protects children up to the age of 13, so is very limited once
children are out of the primary grades (CEPAL, 2015, p. 10). Furthermore, the
only real protection that seems to be available to parents is opting out of the
use of technology devices provided by schools and districts. This brings up
other, very real implications concerning the equity of technology availability,
especially at high poverty schools where many, if not most, families do not
have reliable access to the requisite technology. A product from this portion
of the class is an infographic we created that would allow us
to share some of the concerns that may affect students online.
Lastly,
we created a webquest that allows students to do research about a topic
relevant to the content of our classes. For my webquest, students are asked to research about
the history of math. The students are researching and then creating an argument
to show that the mathematician chosen is the best mathematician in history.
This project allows students to look at a different aspect of math and get into
the lives of mathematicians (which, believe it or not, are often quite
intriguing). Being able to figure out how to incorporate technology into our
classes in a genuine way to deepen understanding or appreciation for our
subjects is a great way that will help us connect with our students throughout
content areas.
Arroyo,
I., Woolf, B.P., Burelson, W., Muldner, K, Rai, D., Tai, M. (2014). A
multimedia adaptive tutoring system for mathematics that addresses cognition,
metacognition and affect. International Journal of Artificial
Intelligence in Education, 24, 387-426.
Gunn,
T. & Hollingsworth, M. (2013). The implementation and assessment of a
shared 21st century learning vision: a district-based approach. Journal
of Research on Technology in Education, Vol. 45 (Issue 3), p201-228.
Johnson, D. (Sept. 2013). Good technology choices: a team effort. Educational Leadership, Vol. 71 (Issue 1), 80-82.
Johnson, D. (Sept. 2013). Good technology choices: a team effort. Educational Leadership, Vol. 71 (Issue 1), 80-82.
Sherman,
M. (2014). The role of technology in supporting students’ mathematical
thinking: Extending the metaphors of amplifier and reorganizer. Contemporary
Issues in Technology and Teacher Education, 14(3), 220-246.
Center for Education Policy and Law (2015). Legal Implications of Using
Digital Technology in Public Schools: Effects on Privacy. San Diego,
CA: University of San Diego.
Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. Proceedings from TSG 16: Research and development in the teaching and learning of calculus. ICME 11, Monterey, Mexico.
Robin,
B. (2008). Digital storytelling: a powerful technology tool for the 21st
century classroom. Theory into Practice, 47, 220-228.
Starkey,
L. (2011). Evaluating Learning in the 21st Century: A Digital Age Learning
Matrix. Technology, Pedagogy and Education, 20(1),
19-39.