Final Post...Final Project

Link to Technology Integration Matrix

                Information is all around our students, and it is important for them to be able to critically analyze and interpret what they read and see. This lesson, about developing a line of best fit, does just that, with a new-found leaning toward technological literacy. In redeveloping this lesson plan, I believe it now hits all essential aspects of literacy (access, analyze, evaluate, communicate and produce) and does so with an appropriate level of technology.

                This lesson for eighth-grade begins with a “Do Now” activity projected on the SmartBoard that will address the first part of the first mathematics standard regarding creating scatter plots. It will be a list of data with an independent and dependent variable and students will have to plot the points on a sheet of graph paper. One student would come up to the SmartBoard to plot their points as a solution to this activity. The “access” part of this standard comes from familiarizing students with the many data sets made available from Iowa State University located here. I would ask students to pick a data set they are interested in viewing as a class (being sure to avoid the three data sets they will explore later in class), and we would create an Excel spreadsheet where we could create a table and scatter plot. We would then look at the data from the perspective of correlations and open up a discussion of what a positive, negative or no correlation data set would look like.

                I would then transition into the main part of the lesson, which is determining a line of best fit. I would use a SmartBoard presentation with student interaction and questioning throughout. The presentation would focus on the plot of one data set consisting of about 10 points. On the SmartBoard, I would draw about three or four different “lines of best fit” on the same scatter plot (two terrible fits, one okay fit and one great fit) and generate a list of criteria the students come up with for what makes a line a “good fit”. As a class, we would then estimate two points that fall on the line to generate an equation for this “informal” line of best fit. I would then put another data set on the board and have one student come up to draw what they would consider to be the line of best fit. Another student would come up to the board and be asked if they agree or disagree with the line. If they disagree, they would draw another line. If they agreed, they would estimate two points and generate an equation for the line.

At the conclusion of this part of the lesson, I would end with showing students how to perform a more formal linear regression on both their calculators (using a virtual calculator on SmartBoard) and in Microsoft Excel. By this point, the mathematics standard is more than met because students are familiar with and have created informal lines of best fit. The technology encourages critical thinking because there is clearly more than one way to attempt a problem such as this, and each one uses a different form a technology. It will be up to the student to determine, from the knowledge they acquired during this lesson, which method is most appropriate for them. All of these techniques, both the formal and informal, would be integrated together in the evaluation, communication and production piece of this lesson.

                The final task I would give students is group work in the form of a performance task, which would conclude this lesson and be assigned for homework either as a long-term group project or take up another class period or two as an in-class project. Performance tasks are often underused in mathematics classes, but as I have learned more about them since I first wrote this lesson plan, I think they can serve as a great, interdisciplinary way to bring technology into the classroom. Not only do they serve as a way to evaluate understanding of the mathematics concepts, but can be a great way to judge student knowledge of technologies needed to be successful in the 21^st century, particularly in the workplace. The premise of this performance task would be that students will be serving as data analysts for a client of a consulting firm and must perform several types of linear regressions discussed in class in order to advise of any relationships in the data and predict any future outcomes. Students will be directed to one of three Iowa State University links that have real-life data sets in them which can be used for linear regressions. They are: catalog print run versus orders, poverty, unemployment, murder rate, gas consumption versus local conditions. After choosing one of those data sets, they will be given instructions that are specific to their data set. However, the first step, regardless of data set, will be to identify an example of who may have provided that data (i.e.- an example of a business, community, etc.) in order to determine who they are serving as consultants to. Students would then perform a linear regression (the exact variables for each data set they would be focusing on would be outlined in the data-specific worksheet) by hand, with Excel and in the TI-83 calculator, keeping track of the equations of the lines and how closely they fit the actual data set. Students would then produce a written paper in Microsoft Word that includes all of the linear regressions (noting which is most appropriate) and an analysis of correlations, predictions of future outcomes and any other information students deem useful regarding recommendations for improving the data (if improvement is necessary). They would also be required to develop a strong argument using research (internet database, journals, etc.) as to why any potential relationships in the data exist. Additionally, the document would have to include any Excel charts and graphs they created with the appropriate and necessary labels and explanations.

                I strongly believe that this new and improved lesson effectively and appropriately uses technology and improves the technological literacy of students in the class. Each of the standards is clearly reached because of the strategies employed and the specific technologies that thoughtfully and fully support each of them. I included standards outside of the required mathematics and NET-S because I firmly believe that educators must prepare students to enter life as a productive member of society through the all-important 21^st Century Life Skills. Those standards serve as a great way to bring mathematics and NET-S standards to life in a way that is relevant to students.

Online Charter in NJ?

If you have been keeping up with education news in New Jersey over these past few days, no doubt a big topic of discussion has been the revolt of parents, teachers, students and administrators in Teaneck against the creation of a digital charter in that school district. If you are interested in reading about the story, you can do so here. The article I will be blogging about is located here and is about the "largely untested" nature of digital charter shcools.

According to the founder of the Garden State Virtual Charter School, the main goal of the potential school would be " to provide a high-quality option for children statewide whose lives don't fit the traditional school setting". I was intrigued by the story of Karen Ryd's son who attending a digital charter school in Colorado. She states that "the charter helped her older son graduate last spring; he needed to work at his own pace and required her one-on-one help for about three hours a day." I would question though: "Yes, he graduated, but at what level did he graduate? How do his skills compare to those of his peers in a traditional school? What curriculum did he cover in the charter?"

As the article points out, the only truly substantive study regarding the answer to this question was done just this year by Stanford University. The results were that "cyber students had significantly smaller gains in reading and math than their traditional-school peers." Yes, I agree, this only one study and should be examined with extreme scrutiny, but the fact remains that this is a very experimental type of school, and their effectiveness must be questioned.

I also wonder that if parents who think their students work best at their own pace are pulled out of public schools, who will be left in public schools? Will public school teachers be left to teach only students who have behavior problems and those who have no motivation to learn?

Finally, I think resources like the Khan Academy can serve as a way which public school teachers can incorporate some ideas of self-paced learning in their classroom. However, this is up to the individual teacher, their circumstances, philosophy and, ultimately, the wants and needs of the students and parents.

What Do YOU Want to Learn?

In reading this blog post on boston.com titled "Some Lessons for Virtual Learning", I came across a great resource: The Khan Academy. According to the Khan Academy website, it contains "over 2,700 videos covering everything from arithmetic to physics, finance, and history and 253 practice exercises". Just briefly looking at the site, one can see it is possible to learning something about topics ranging from the Geithner Plan to solve the banking crisis to Differential Equations to Healthcare to Investing.

Not only does this resource allow us, as educators, to learn more about topics we are interested in, or else watch a short video to refresh our minds on something we learned a long time ago, but it can provide a great resource for our students. As the blog post states: "The data from Khan Academy shows that, with self-paced learning, a lot of kids who would have otherwise been relegated to slow-learner status actually catch up to and outpace the supposed smarty-pants in the class." Yes, it would be great to have independent research done on this topic, but the potential for a site like the Khan Academy is truly endless. It truly is remarkable that not only can a student get instruction from you, their teacher in class, ask for help outside of class from you, be given workbook homework for enrichment, and then, watch a video in the comfort of their own home to further their learning.

No doubt, there must be some "quality control", where the teacher will need to judge the appropriateness of a video in the course of their class, but it can be a great resource to refer students to that are struggling with a particular topic, or else may want to move on to more advanced topics.

The Khan Academy is growing too, so I suspect that we will hear much more about it in the future. The blog states: "The free Khan Academy has provided almost 100 million exercises, now boasts about 3.5 million discrete users, and is growing at a rate of about 300,000 users a month (with the pace of growth increasing)". I encourage everyone to check out this resource, either for a potential link to share with students, or as a break from your regular coursework where you can explore some areas or topics of personal interest.

“Online learning as an alternative to a violent in-school experience”?

Gail Collins always seems to write an interesting editorial piece for The New York Times. This one, entitled "Virtually Educated", is no exception. In it, she refers to a recent development in Tennessee, where students in one county were given the option of leaving their current school district to attend an online-only charter school run by the company K12 Inc.

What was interesting about this, and I really hate to bring in politics, was the fact that they picked, of all places in Tennessee, an area with a lot of poverty-stricken families. As Gail Collins points out, on the K12 website, the online school headmaster touts her school in this fashion: “online learning as an alternative to a violent in-school experience”.

Does anyone have any thoughts on this? Will this situation in Tennessee be a wake-up call not just about issues with our education system, but, more generally, social injustice and inequality? I honestly never thought of technology in schools being used in this manner, and am still trying to gather all my thoughts. I just found the editorial to be extremely interesting and enlightening--I just could not help but share it.

Timeline of Classroom Technology

The Globe and Mail out of Canada has a very interesting timeline of technology in the classroom. It starts off with BCE technologies, like the papyrus, abacus and quill pen and culminates with modern technologies like the iPad and the "Flipped Classroom", which was a totally new concept to me. I was very much intrigued by the idea of students watching lectures online at home and having class time used instead for one-on-one practice with the teacher.

Other highlights of the timeline for me which were somewhat math-related include the overhead projector (which I just used substantially in a lesson I taught), calculator and the interactive white board. I was also fascinated to read the description of the Personal PC:

When 17 Ontario high schools were hooked up with 8-by-10-inch computer screens and monitors, Douglas Penny, then director of the research and evaluation branch at the province’s Ministry of Education, found it necessary to dispel fears that computers would replace math teachers.

The most interesting part of that to me is no doubt the fear of computers replacing math teachers. As we know, this has definitely not been the case. Not only have personal PCs not replaced teachers, but I think they have served as an excellent tool in the classroom for instruction. They allow the teacher to integrate multiple learning styles through a choice of interactive programs and visual/audio representations, as well as bring real-life programs and models into the classroom that would not have otherwise been possible.

Interactivity #5

Updated Spreadsheet

When I reflected upon the work I did for my previous interactivity, I discovered a lot of areas where I could have made substantial improvements. In my revisions, I sought to emphasize the importance of a mixture of whole class discussion, individual work and group work using a variety of technologies, particularly, the overhead, internet, Excel and the calculator. I also flushed out the strategies I thought the lesson was using by adding more detail and writing more about the intent of the strategy in achieving the standard. This also meant speaking more as to effective uses of the technology noted in the next column in the corresponding strategy.

If there was one technology in particular I wanted the revisions to emphasize, it was Excel. I think the case of any kind of data analysis, Excel can serve a vital tool in not just representing data, but performing calculations and regressions that give students a greater insight into what the data actually means. If the lesson can effectively incorporate these aspects of Excel, along with a student-applicable real-life scenario, I think it becomes all the more stronger.

Much along the same lines, if time permitted and the lesson could be extended, I would very much like to send students out to collect their own data for a scatter plot. Student-collected data just feels much more organic and relatable to students. It also would present a great opportunity for students to learn more about a major player on the internet (ebay.com), as well as how to collect, interpret and classify user-collected data. Any experience that can further strengthen students’ 21^st-century life skills is definitely a must-do in any classroom.

In terms of copyright and fair use issues, the only major ones were those involving short-length printed material, software and the internet. As mentioned in the spreadsheet, the use of the worksheets and overhead sheets in this lesson is covered by law. A teacher would be allowed to make enough copies for his/her class, and in turn, the students could also incorporate the worksheets and such in any projects. Another issue was that of legal and licensed copies of Excel. As pointed out in the readings and videos for this interactivity, software used in the classroom must be purchased and licensed legally. If I suspected this was not the case, I would be sure to check the status of the program with the school administration or district, if need be. Finally, if students or myself incorporated any aspect of, in the case of this lesson, ebay.com, it must be properly and legally presented. If data is gathered on bids or other ebay.com related features, specific dates must be noted, as well as the particular link where the information was gathered from.

The Next Time You Get That iTunes Giftcard...

think about purchasing a Math App from the Education App Store (http://www.apple.com/education/apps/). Unfortunately, I don't own any Apple products, so I am unable to actually try out and test some of these apps, but it really intrigued me that there was a market out there for math-based apps. Not only can you turn your iPod or iPad into a basic calculator, but through these apps, it can be transformed into a graphing calculator, an interactive manipulative to aid in learning algebra or even a "chalk board" that can be used to learn and practice arithmetic.

I can definitely see there being a large potential for these kinds of apps to play a role in the classroom. Students are glued to these kinds of technologies, and if educators can tap into this successfully, students can take materials used in the classroom home for additional practice outside of the traditional textbook homework assignments.

If anyone has any experience using any of these math apps from the iTunes store, I would really like to hear about it.