Katherine
J. Huber
Reflection...
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| Overview | ||||
| Narrative | ||||
| Exhibits | ||||
 Reflection |
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My overall experience with the MiTTEN program has been outstanding. Technology integration has been a means of reaching students who otherwise may have struggled in the classroom, either from an academic or social perspective. Many of our students have had good personal experiences using computers and were at their best in the computer labs. Technology gave those students an opportunity to shine where they may otherwise have failed in a traditional setting. In the best cases, these students helped their peers learn techniques that seemed to be almost second nature to them.
Technology integration has enabled me to provide exploratory lessons that reinforce content areas. This strategy transfers the responsibility of teaching from the teacher to the student - it enables the learner to construct their own knowledge. My cooperating teacher and I attempted to design lessons that were rich in content, engaging for the students, and practical.
Below you will find my reflections. Not everything went right, but in the process, I believe our students learned more about mathematics and technology, and I believe I learned more about the software, the logistics of good technology integration, and effective teaching strategies.
- How did the use of technology help my students learn this subject matter in a way that is more effective or would not have been possible otherwise?
- The Function Families lesson was perfect for technology integration. Our Algebra I students have not yet learned how to work with quadratic equations, nor have they learned the characteristics of linear equations. They understand the concept of absolute value but have not been exposed to the graphs prior to this lesson. Consequently, our students did not have the tools required to graph equations and make conjectures about their characteristics. Using technology enabled our students to enter functions and easily graph the equations using Geometer’s Sketch Pad features. In this way, they could quickly create and study the graphs, categorize them, and make conjectures. All of our students were able to identify the characteristics of quadratic, linear and absolute value functions do to their ability to explore many equations in one 50 minute class period. Without technology, we would have had to present the functions and their graphs while students passively took notes. Technology integration enabled students to actively investigate while the teachers guided the process. This was a great lesson!
- Unlike
the
Function Families lesson, students
had been exposed, prior to integrating the
technology, to data collection, plotting ordered
pairs, the basic concept
of
correlation, and estimation using manually created scatter plots.
Students were asked to
compare and contrast their manual graphs and their predictions with
those
created using FATHOM. Our goals were to
reinforce graphing while highlighting the increased precision available
through
technology. FATHOM will generate a least
squares line and a correlation coefficient for paired data. This
feature gave us the opportunity to
discuss correlation in more detail without going through the mechanics
of
deriving a least squares line and correlation coefficient by
hand - tasks that are too advanced for our Algebra I students.
- My
favorite part (and
the
students’) of
the Probability lesson, was the simulations. Students
could explore the results of a large number of trials very
quickly. In this way, they were able to experience the effects of
sample size rather than being told the effects. Very nice!
- Graphing Functions and Their Derivatives was a great lesson and one of my favorites because of the great benefits to our students. The typical routine for our AP Calculus students is to take notes while listening to the lecture and subsequently, do the assigned problems. This lesson gave students the opportunity to visualize what they had been learning in the classroom. I was amazed at the lack of understanding when students first started graphing functions and their respective derivatives. Doing problems on paper is one thing, but creating and seeing the representations was entirely different. Technology enabled us to graph many functions and their derivatives in one 50 minute session. The students could not have accomplished this by hand. This lesson is a must for AP Calculus students.
- What worked and didn't work in the planned lessons?
- You will notice the lack of student work for our first lesson, the Function Families lesson. This is a result of my inexperience with technology integration and with portfolio development. I did not determine the logistics related to capturing student work until our next technology integration lesson. Recognizing this omission, my cooperating teacher and I set up a universal drop box (drive), provided by the district, for students to deposit their work. This worked great for future lessons.
- The Writing and Mathematics lesson did
not work as envisioned. Students were given three journal
questions
to be completed using MS Word. Most
students were familiar with the software and the functions of MS Word
made
writing efficient. However, it was very
difficult to give our students timely feedback in order to stimulate
improvement. Nonetheless, our students did
show
improvement in there writing according to an analysis we conducted
using
- Rigid Transformations was a good lesson and fun for the kids. It was good because it was an efficient reinforcement of what we had been learning in class. The mechanics behind creating points, lines, reflections, transformations, and rotations, using Geometer's Sketch Pad, are more involved than those for graphing a function. Students had to be more deliberate to complete the task thereby, creating some anxiety which theorists claim aids in the learning process. We created a pre-lesson to give students an opportunity to learn the software prior to this lesson. I recommend this if your students are first time users of the software. All of our students completed this assignment, producing quality work and performing well on a subsequent examination.
- The AP Calculus
curriculum is rigorous and fast paced. Students in this class
solve
lots and lots of problems - someone else's problems. During the
Related Rates lesson students used an electronic discussion board to
create and post
related rates problems of their own. Each student was required to
answer someone else's problem, and check and comment on the response
they got to their problem. This lesson engaged all students, but
further required that they examine multiple problems and their
solutions before selecting one to respond to - tricky, wouldn't you
agree. Having students create and check problems
requires higher order learning skills than does answering textbook
problems. There was
minimal downside to this lesson. The only problem we encountered was
when a couple of students had difficulty accessing the U of M - D VLT
system - nothing a little coaching didn't cure.
- All of the lessons highlighted in question #1 worked well for the reasons discussed.
- What would you change to improve the lesson in the future?
- The lesson on matrices required too much data entry. I was eager to expose students to MS Excel because this is commonly used software in business. I was also eager to use a business model, Profit = Revenue – Cost, because several of the students who were not connecting in the classroom environment had expressed ambitions of running their own businesses after graduation. I had developed a hypothetical business with twelve months of revenue and twelve months of cost. Students were expected to develop a profit matrix. They did this but there was too much data entry. Students could have computed a large number of smaller matrix addition and subtraction problems by hand in the time it took them to enter the data. Changing the business scenario to quarters, as opposed to months, would have made this lesson as effective and more productive.
- The lesson on probability was too long. Students could have used at least one more day in the computer lab to complete it as designed. I would eliminate some of the exercises so the lesson could be completed in two lab days. For most of our students this lesson was their first exposure to probability. Students were researching information and answering questions to complete a task. Our probability quiz revealed that little learning actually took place. The basic concepts of probability should be discussed with students prior to going into the lab.
- Our students loved using Power Point for a chapter review. This lesson appealed to our students' creative and social needs. A hard copy of all the presentations was given to each student for their review. It gave them yet another means of test preparation, reinforced the content, and gave our students practice presenting to a group. We assigned each group a section of a chapter out of their text. As such, each group became somewhat expert on their section. I compared the results of this chapter test to those from prior years. There was an increase in the average test score, but not a statistically significant improvement. Next time, I would require each group to create questions or sample problems for the audience to solve. This would actively engage the audience in each section rather than just their own.
- How has teaching this lesson changed the way you think about integrating technology into teaching?
- I really
like MS Excel because of the variety of features and applications,
because graphs can be customized and made presentation-ready, and
because
of its wide application in business - and I am very proficient with
this software. I had used Geometer's Sketch Pad (GSP)
previously, but limitedly. My cooperating teacher, being more
familiar with GSP and less familiar with MS Excel, suggested that we
use GSP for the Family Functions lesson. This was a smart
decision because GSP graphs functions with a click of an icon.
The user does not
have to enter data and set parameters in order to graph as they would
using MS Excel. They
simply enter a function, such as f(x) = 2x + 5, and select the graph
function - very nice for the beginning grapher. I was able
to see the benefits of using other software, where I previously would
have used MS Excel. The value of the lesson would likely
have been lost in the technology had we used MS Excel. This was a
very valuable lesson for me.
- I had observed,
early in the semester, that many of our students had not acquired good
study techniques and
habits. I
hadn't previously thought of technology as a study tool until we
designed a chapter review using Inspiration®. This
project was
intended to help our students prepare for a chapter test. I
think many
of our students' only preparation was the construction of this
web despite our encouragement to use it as a study
guide. Good study
habits, like content, need to be learned. This project gave
students a strategy they may not have considered, especially for
mathematics. It was fun, appealed to students' creativity, and
was useful. I will integrate technology as a means of
introducing a variety of organization and study techniques in the
future.
- As a
result of this experience, what learning (both formal professional
development and informal self-teaching) do you think you need to
continue your professional growth?
- I did not grow up
using graphing calculators, as do many of today's high school
students. My first exposure to this technology was during a
recent math methods class. I want to increase my
proficiency with graphing calculators and explore the many peripherals
and software that can be used with them.
- I would like to
learn how to develop my own Java programs and applets. I have
found applets that are exactly what I needed to demonstrate a concept,
and in other cases, I have had to change my approach to coincide with
the applets I was able to find. It would be great to be
able to design and create applets that are exactly what my lessons and
students need.
- I will be
developing a teacher website to communicate with and offer educational resources to
students, parents, and the community.
- I have talked to several teachers, recently, with the opinion that students get enough exposure to technology outside of school and that integrating technology into the classroom is too time consuming given the vast material students are expected to learn in such limited time. These teachers prefer to teach the curriculum using traditional methods. Clearly, this was not my experience during the MiTTEN project. I am interested in researching and writing journal articles regarding the effectiveness of technology in the secondary mathematics classroom, and in general, becoming a technology advocate through my actions and students' results.