Wicked Problem Project: Part B - Application of TPACK

What is the TP knowledge for the solution?  (i.e., how does the technology you have chosen support the teaching strategies and methods you have chosen?)

The Wicked problem I have chose has a somewhat unorthodox pedagogy associated with it.  The content will not be delivered by a classroom teacher but instead will be delivered by two interventionist who will be pulling students throughout the day from classes other than the students’ primary math classes.  As such, the solution must allow students to enter and leave the intervention at any point.  The goal of the intervention is to increase achievement in a student’s current math course.  Another layer of complexity is attributed to the fact that we do not use textbooks in out Algebra 1 and Algebra 2 courses.  Instead we have a series of assignments that are meant to allow students to build their own knowledge of mathematics rather than having a book or a teacher as the authority.  When students take charge of their own learning and are the ones who control the direction of their learning they achieve more than those who simply memorize a series of facts that to them are discrete and disconnected.  We find that many students struggle in transitioning from having math content dictated to them to being responsible for generating their own ideas about it.  As a result they do not engage in conversations about mathematics in the classroom and wait for others to do most of the thinking. 

The technology that I choose to address these issues is a website that contains learning modules.  There are several reasons that make this technology a good fit for the pedagogy.  First, it allows students to access material throughout the day and allows them to access to material after school hours as well.  This is important to our pedagogy in the sense that students can be pulled from another class to work with us on issues that the classroom teacher deems necessary.  The intervention is allowed to take place for as long as necessary in order to help the student achieve.  More importantly we can put them in apposition where they are responsible for building their knowledge.

Central to the TP portion of this discussion is that a website allows us to produce, store and display content that matches the way we teach.  Currently our district is spending large sums of money for a software package that claims to be aligned with the Michigan High School Content Expectations, which is disputable.  What is not in dispute is the fact that it is not aligned with the way we teach, and therefore only reinforces the students beliefs that mathematics is something that is to be memorized and not engaged in.  The software seemingly asks students to memorize rote facts and recall them later.  It contains assessments that are multiple choice and really allow the students to guess their way through the material.  While there are times when we need students to know and use algorithms, we usually ask students to derive them.  When assistance such as the one provided by our districts software are used we send students the message that what we really value is their ability to memorize an algorithm.  When students return to their classrooms they take the idea with them and the cycle repeats itself.  Creating our own website allows us to have complete control of the material we use and allows us to be sure that it matches our pedagogy. 

It is difficult to separate the content from this part of the discussion but part of the content that is planned for the website is directly related to the TP part of the discussion.  Overwhelmingly teachers responded to a survey that I sent out to them by saying that one of the biggest obstacles that they see for their students is lack of engagement in the curriculum.   One module will be devoted to student learning habits in an attempt to help them understand what is required to be successful in their math class.

What is the TC knowledge for the solution? (i.e., how specifically does this technology make the content in your problem more intellectually accessible?  Be sure to think about representation.)

It is difficult to separate the content from the TP part of the discussion because I see the content and pedagogy are so tightly intertwined in my mind.  The planned content for the website is directly related to the TP part of the discussion.  Overwhelmingly teachers responded to a survey that I sent out to them by saying that one of the biggest obstacles that they see for their students is lack of engagement in the curriculum.   One module will be devoted to student learning habits in an attempt to help them understand what is required to be successful in their math class.

Since the content related to the Wicked Problem is the entire Algebra 1 and Algebra 2 curriculum it is difficult to discuss specifically why the chosen technology is a good match to a specific area.  What is true about the chosen tech is that it allows for multiple other technologies to be used within it.  Instead of discussing the entirety of the problem we can look at how a module may play out.  The results of the survey I sent out also indicated that students have difficulty transferring between the representations of a function (Table, Graph, Rule and Verbal-Written).  A part of the module devoted to exploring these ideas might be a time lapse video where students are asked to record their ideas about what things the can measure that are changing.  They could also be asked to think about way to show how two of the things that noticed change.  More pointed questions like pick two things that are changing and make a table are also possible.   This same module may contain more directly targeted ideas like a StAIR where the students would be asked to take a table, make a graph from it and explain how the two relate.  Each module would also have an assessment at the end to give us and the student feedback about their progress.  A Google Docs Form could be embedded for this purpose.  A link to a Jing presentation about how to make a rule from a table could also be included.  The list above is my brainstorming about how the particular content we are interested in is connected to the technology.  The format of a website allows for complete flexibility to add many different types of experiences for the student to help them engage in the content more fluently.  While the idea of student learning styles is not the only way that students can learn the website also provides for an array of learning styles to be addressed.

What is the PC knowledge for the solution? (i.e., how specifically do your pedagogical choices make the content in your problem more intellectually accessible?) Be sure to think about how the student will experience the content given these instructional strategies.

I touched on this idea in the both previous sections.  Where our program differs most significantly from my perception of other mathematics programs is that we do not teach a skill and teach how it is connected to other ideas.  Our goal is to have students come up with ideas for how to deal with problems that is directly linked to other things that they already know.  They may then develop skills as a result of a deeper understanding of the mathematics, but it is meant to be grounded in understanding, not memorization.  We often provide situations where we expect particular mathematics to be “discovered” as a result but the questions are open and not scaffolded to the point where students are left with no other choice but to do the things we want.  This kind of thinking by students is uncomfortable for many of them and they struggle as a result.  There is a need for students to have extra practice in thinking through this type of problem, as this is what is expected of all students in the classroom.  For some students the extra chance to experience the content from their classes again may aid in their understanding and proficiency. 

We also know that having multiple means to access content is helpful in allowing students to access the mathematics.  Many students may also find that interacting with a computer allows them to move at their own pace through material as opposed to what they may experience in the classroom.  Many students lack self assessment skills which would be a tenant in any of the content that is presented in the modules.   It is hoped that students will be able to see some success with mathematics in an environment that is nonthreatening and not directly tied to a grade.  They can experiment with their ideas and build new ones without having to feel as though others will judge them for their responses.  This is where I take on a very active role with students, encouraging them to work with the content the way they would be expected to in their actual math class.