The Problem:
The problem facing our district and likely many others is that students who struggle in their mathematics classes. Often these students reach a point where their self efficacy becomes so low that they give up, resulting in failing multiple trimester of Algebra 1. The consequences of this are wide ranging and include students not graduating on time if at all, schools failing to make AYP… clearly in the context of No Child Left Behind the last outcome is unacceptable but more importantly as educators we know that the prospects for these students is bleak. In an effort to increase student achievement my district has dedicated four hours of instruction time for interventions with them. The teachers will work with students in some way to promote success in their current math classes. The additional constraint was added that the class must be technology based.
The Solution:
We will use a math lab that is technology based, with the goal of helping students be more successful in their current math classes. The lab is scheduled to be staffed by two math teachers and cover 4 of the 6 hours in our day. The lab consists of a classroom with laptops where students will work on assignments determined by their current math teachers and the lab supervisor.
We decided that we did not want students assigned to the course. This had been tried previously and the classes ended up becoming populated by groups of students who actively sought to undermine the purpose of the class. The proposed system allows us to bring students into the lab as needed by calling them out of classes other than their math class or other required courses. Unfortunately this means that students will be brought down during their elective periods. It is certain that there will be teachers of electives who are unhappy about having students pulled out of their classrooms. This is not a statement that elective classes are less important. To the contrary, under the current system students who fail end up having reduced choices of electives, as they end up filling their schedule with retakes of required courses. It is our belief that this will be mitigated by the fact that students passing their math classes should have more slots in their schedule for electives later. Additionally, we do not intend to pull them from any class for weeks at a time and it is planned that they should be able to continue with the coursework of any elective that they miss.
In order to reach as many students as possible we have decided to construct a website that contains a series of learning modules or groups of content geared toward helping a student with a specific goal. We will facilitate their learning by monitoring their progress with them directing them to particular resources while at the same time building mentoring relationships. The modules will do the majority of the work with the mathematics content. We will do the management work and assist with the mathematics as necessary.
What we will be looking to see is if we are able to lower our failure rates for starters. This is easy to measure because it is quantitative. A more difficult thing to measure will be the behaviors’ of the students we work with. It is hoped that we will have an impact on their attitudes toward school and math in particular.
TPACK:
Technology and Pedagogy: The main issue here is that our chosen pedagogy requires students to use higher order thinking skills and engage in doing mathematics not just memorizing algorithms and facts. As such it is imperative that we select a technology that supports this view. There are various pieces of software that exist to help students pass math courses, however they seem to share the notion that mathematics is about process and memorization. In order to remain true to a constructivist pedagogical model a technology must be chosen that allows us to author content to address the issues of our learners. The technology must also be flexible enough to allow different learners to access a vast array of content at different times. A website is one such technology. In addition to meeting all of the criteria described above it has the added benefit of allowing many other technologies to be used through it, such as blogs, embedded videos, links to other websites etc. As excusive authors of our own content we are able to help ensure that the experience that students get is consistent with what is being done in their regular classroom
Technology and Content: What is true about a website 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. Lets say for example students are struggling with the notion of a function. 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. After any activity students could be asked to respond to a series of questions about their learning. 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 technology allows for almost any content topic to be covered in this way. 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.
Content and Pedagogy: Where our program differs most significantly from my perception of other mathematics programs is that we do not teach a skill and then try to 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.
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