Month: July 2016

Module 3 Reflection -Connecting the Dots

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The module title “Connecting the Dots” is very appropriate and closely mirrors the path I find myself walking. I started this class with a basic knowledge of the major learning theories: Constructivism, Cognitivism, and Behaviorism, and a much narrower understanding of Connectivism. Researching and reflecting on what happens in my classroom (Cognitivism) versus what happens in my head and heart (Constructivism) led me to Gardener’s Theory of Multiple Intelligences. As I have continued to research, I found several areas that interested me, but the one that spoke to me most was Carole Dweck’s Growth Mindset Theory. My students come to me firmly believing that they are bad at math, that they can’t do it, and there is nothing that either they or I can do to change that. Towards the end of a particularly difficult time last year, I started doing some reading on this subject. I need to find a way to convince my students that if they put the effort in, they can be successful. My telling them so is not enough. As often happens, school ended, summer school started, grad school continued, and I stopped thinking about this with any real seriousness. Enter this module. Isn’t it wonderful when one can align what one is learning directly with something needed, something that can be used and applied almost immediately? Even better, next year I add 8th grade to my schedule and will soon teach 7th grade as well. I can’t wait to see what my classes will look like when next year’s 8th graders enter my 10th-grade classroom three years from now. I dream about the possibilities of teaching a group of students who not only believe they can learn, but are willing to work towards that goal.

Dweck believes that intelligence is not set at birth, that the brain can be exercised just like any other muscle and will show growth when this happens. According to Dweck, “When students believe that their intelligence can increase they orient toward doing just that, displaying an emphasis on learning, effort, and persistence in the face of obstacles” (2008).  She has written numerous books and articles on mindset and motivation and has created and participated in many studies. Unfortunately, many of the studies I read, while interesting, do not include enough students to be statistically valid. The studies that have enough participants are often inconclusive. One study, in particular, showed that while it is possible to change a student’s mindset from fixed to growth; without ongoing interventions, the mindset reverted to the original within a relatively short period of time. The ongoing theme throughout the articles I found is that more and better research is needed.

There are few scholarly articles written about the use of technology to create growth mindsets. Dweck created the Brainology program, a series of modules designed to foster the growth mindset in students. This program appears effective, but there is not much information on the longevity of any change. Since the Growth Mindset Theory fits well within Constructivism, project-based learning and maker spaces are two good examples that will allow students to use technology to actively create hypotheses and find ways to prove or disprove them. These types of learning demand deeper thinking and perseverance from students.dreamstime_xs_48879005

Many of the articles I read mentioned the impact of the teacher’s mindset on his or her students. Most claim that if a teacher has a fixed mindset, it will detrimentally impact the students in that classroom. Some argue that the teacher’s mindset is of little importance. Again, there is a call for more research. I don’t see how a teacher’s mindset could NOT impact the students. If I don’t think that mindsets can be changed, I am not going to use language and activities designed to promote growth. Mathematics is an area in which many students demonstrate fixed mindsets. As I stated above, this is the most prevalent thinking that I see. My students are very quick to give up, often asking for help after that first glance at the activity. My use of interactive notebooks (see here)has had a slight impact on this attitude, and my hope is this impact will continue to grow as I add other grade levels to my schedule. The chance to have my students for four or five years in a row will allow me to introduce and foster the attitude that we can “change your mindset, change your mind”.  It will allow me to introduce them to project-based learning, knowing that even though in 7th grade it will be new, awkward and uncomfortable, by the time a student reaches 10th grade it will be business as usual. My efforts to incorporate student-centered activities have been largely unsuccessful with students whom I only see for a year to two. Instead, I have tried to focus on my language and how I say things. Below are some examples of my thinking that are posted on my classroom walls. The attitude bulletin board can be found on the site Math=Love here.


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Dweck, C. (2008). Mindsets and math/science achievement.


Module 2 Reflection -Philosophy of Education

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I found this module to be very overwhelming, like trying to take a sip of water from a fire hydrant. It has been a long time since I thought about educational philosophies and how my beliefs and processes fit within them. The week that I have spent researching, reading and thinking is not enough. I need to make time to continue this reflection, as I suspect that, for me, there will never be a final answer.

I have always leaned toward constructivism. I believe in student-centered education, and using real world problems to drive instruction. But the reality of my classroom does not reflect my beliefs. It shows that while I may be a Constructivist at heart, my classroom demands a more Cognitivist-Behaviorist point of view. By the time my special education students meet me in 9th grade, they have been learning in self-contained classrooms for nine years. They find it difficult if not impossible to function when they are not given step-by-step instructions. Any attempts to add more constructivist types of learning are met with strong resistance, if not outright refusal. Part of the problem is that many have huge gaps when it comes to their knowledge of mathematics. They are trying to climb a staircase and steps 3,4 5, 7, 9 and 13 are all missing. How can I expect them to be curious and self-directed when they don’t even understand what to be curious about?

To incorporate more of my Constructivist beliefs into my classroom, I have asked to teach the self-contained 8th graders, as well as my 9th and 10th graders. This fall will be my first time teaching middle school students. I expect to eventually add 7th grade, which will allow me to teach the same students math throughout both middle and high school. With this level of continuity, I plan to start adding some small projects into the 7th-grade curriculum and slowly working that through all of my classes. By the time I have students in 9th grade, they should be comfortable exploring topics in a self-directed environment. At the very least, I am hoping that the trust levels are high enough to allow me to try more challenging activities, using tasks that require critical thinking. If they know that I believe in them, they might just believe in themselves.

Technology is woven throughout my curriculum. Since all my students have Chromebooks, assigning drill and practice games has become routine. My district uses Google Classroom as our LMS. It is easy to add links to several different games and activities so that my students can practice any skill(s) they need. One thing I would like to incorporate more of is the use of technology to show our thinking. This might mean creating a digital graphic organizer to use in our interactive notebooks. Instagrok, Glogster or Powtoon would lend themselves well to this activity, and we could create a QR code to glue in our notebooks that when scanned would take us back to our digital graphic. Desmos’ Classroom Activity section gives my students the ability to see cause and effect very clearly, by allowing them to change parts of an equation and see the immediate change in the graph.

While researching learning theories to write about, I decided to work backward, looking at what I use in my classroom that I find most successful for the largest number of students and then seeing what learning theory addresses that activity. I started using interactive notebooks two years ago and they have quickly become my favorite way to teach algebra. When I started breaking down what I do when I teach with these, I decided that they are Cognitive in nature, as essentially they are graphic organizers. I landed on Howard Gardener’s Theory of Multiple Intelligences and realized that these notebooks play to this learning theory. Gardener believes that people have many different types of intelligence and  Interactive notebooks play to several of these. As a special education teacher, Thomas Armstrong’s thoughts regarding students being misidentified as learning disabled because they don’t fit our current educational focus on numbers, words and concepts really hit home (Hearne & Stone, 1995), and will cause me to look at my students in a completely different way this coming fall. What if I taught to their strengths instead of focusing on their deficits?

As I look back on what I learned this week, the biggest thing I have taken away from my readings is that learning cannot be boxed into just one theory or school of thought. Different situations, topics, indeed, different students, require different strategies. Learning will be most effective when I use a mix of epistemology, choosing what I need for any given concept. The theories themselves encourage this, as many contain overlapping parts, much like the Venn Diagrams I use in my classroom. I look forward to continuing to develop my belief system as it pertains to learning.




Hearne, D., & Stone, S. (1995). Multiple intelligences and underachievement: Lessons from individuals with learning disabilities. Journal of Learning Disabilities, 28(7), 439-448.      doi:10.1177/002221949502800707

Module 1 Reflection – Educational Technology – Introduction to the Field

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This week we were required to create a personal definition of Educational Technology. It was interesting watching the class thought process as we shared and discussed our definitions. There was a lot of “I didn’t think about that” and “I liked that you included this”. Many of us stated that the discussion was changing our original definitions, adding to their complexity and thoughtfulness. James Finn’s description of technology as a “process and a way of thinking”, rather than a “category of objects” helped add shape to my definition (Januszewski, 2001):

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My first forays into incorporating technology into my classroom consisted of borrowing another teacher’s class set of Chromebooks. They were only available for one of my class periods so that class quickly became my guinea pigs. We created some Google Slide presentations in small groups, played several Kahoots, and used Desmos. I found the whole thing rather intimidating, especially since my students are mostly on the wrong side of the digital divide. Many are not connected outside of school, and most do not have access to a computer at home. At the end of that first year, I found out that my district would be going 1:1 with Chromebooks. While I found that news exciting, (my students would finally be connected, at least at school), I also realized that I needed to learn how to integrate that technology appropriately in my curriculum. To that end, I spoke to one of our IT people who is a graduate of the MET program at Boise State. After doing my own research, this program seemed to be exactly what I was looking for, and I enrolled last summer.

I completed my first certificate last week and am now considered a Technology Integration Specialist. Using what I have learned over the past year has added much to my ability to integrate technology in an appropriate manner. Teaching algebra to special education students presents many challenges, and the use of technology allows me to create knowledge and understanding in places where the concepts are so abstract that my students struggle to make sense of what they are learning. I use a lot of simulations, adding some visual and kinesthetic learning to topics like functions, finding domain and range and What If? problems when we explore graphs. Demos and the Desmos Activity Builder have been invaluable for this type of exploration. I use Google Forms for formative assessment and often use Flubaroo to grade them. All direct instruction is projected through my tablet onto the classroom screen. Students love it when I hand them my tablet and stylus and freeze the screen. As other students work out a problem on paper or a white board, one student works it out on the tablet. When we are ready to discuss, I unfreeze it, and the work is displayed. Interestingly my students don’t see this as using technology. Their version of educational technology is the use of cool tools and fun games that make learning algebra more fun and less boring. Not a terrible definition, but definitely limited.

Learning more about the pedagogy and theories behind educational technology will help me better integrate these tools appropriately, in ways that will best meet my students’ needs. As I progress through this program, I notice that even my language is changing. I am becoming more of a facilitator, asking my students what they wonder when I show them something new. I am more willing to let those awkward silences stretch out a little, and increase their discomfort in an effort to improve their willingness to think on their own and then share those thoughts out loud.

I am already known as one of the more “techie” teachers in the building. My co-teacher and I give presentations at math conferences at both the local and state levels. Our current department chair does not use technology other than a graphing calculator with his students. My hope is that when he retires in the next couple of years, my knowledge, and background in educational technology will influence the new department chair to incorporate technology throughout the department. I also hope that my students will themselves be a catalyst of change. If they enjoy the ways we use technology in math class, I want them to push their teachers to incorporate that technology in other classes. When my math-phobic students tell me they like math because I can make it fun, then other classes that are not so abstract should be able to follow suit.

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Dr. Ray Clifford, 1983



Januszewski, Alan. Educational Technology: The Development of a Concept. Englewood, CO, Libraries Unlimited, Inc., 2001