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Title : Teaching Algebra in the 21st Century Classroom

Ken Miller and Kelly Smith

Description: Methods for Improving Student Engagement with the Use of Technology = =

Table of Contents

Executive Briefing........ 3 Introduction........ 4 Heading 2..... 4 Heading 3.. 4 Analysis........ 5 Audience Analysis..... 5 Environment Analysis..... 5 Content Analysis..... 5 Content Map........ 6 Objectives & Test Items........ 7 Implementation Guidance........ 8 Evaluation Framework........ 9 Prototype Design Specification........ 10

== Analysis

[The ** Analysis ** ** section ** should describe ** three ** things: (1) the ** audience ** ; (2) the ** environment ** in which learning and performance will occur; and (3) the ** content ** the project will involve.

Begin with a brief introduction to this section. ** INTRO=KEN ** And… don’t forget to state the sources of your analysis insights; you want to establish credibility for the data and perspectives you present throughout this section.

Use tables, illustrations, bulleted lists in addition to running text – anything to make your description of the audience interesting, compelling and effective. Said another way, do something to make this entire Analysis section more than a collection of paragraph blocks.]

Audience....(from AUD) [Who are the people this product is designed to reach? Describe them in general, and then give specifics – presenting attributes that are relevant to the product’s design. What interests them? What type of examples or scenarios will read as authentic to them? What is the past experience with content in this general area? Do they have prior knowledge of this content? If so, what is it – and at what level (fact, concept, procedure, principle… apply or remember). Remember to describe their motivation – in terms of value and confidence for this subject matter.]

**Audience**


 * Using Quia as a survey tool as well as face-to-face interviews, we found our audience to be middle and high school teachers of algebra in San Diego, Los Angeles, and San Bernadino counties. With experience varying from 1-10 years, they are currently teaching general math and algebra. Most have small classes under 20. However, one respondent has classes as large as 31-35 students. Teaching three or less algebra classes a day, our audience clearly teaches subjects other than math in their full-time schedule.**


 * In addition to their teaching background, our survey looked at the attitudes and proficiency of the audience, in creating engaging algebra lessons. When asked Table 1-1 identifies how these teachers determine student engagement.

**


 * When asked what percentage of increase in student performance would justify the time expense for training and preparation of engaging lessons, respondents chose 10-20%. One respondent clarified that he would be willing to put in any extra time for even the smallest increase in performance.**


 * Although feeling adequate about their ability to engage their students, a majority of the respondents feel that it is possible to make any math topic engaging. When given a list of algebra strands,** //**graphing linear equations, the Pythagorean Theorem, factoring, and word problems**// **were selected as one of the most applicable to student engagement. Least applicable was** //**quadratic equations**// **and** //**square roots**//**.**


 * To identify any skills-knowledge deficit in regards to possible engaging technologies, survey respondents ranked their proficiency with different medium. Table 1-2 presents selections.**


 * Table 1-2**

**Two respondents wanted to know more about using computers with math instruction as well as math projects in a technology lab setting.**

**Environment**


 * The training environment of our web-based course will involve teachers using single-user computer stations. Reliable Internet access is a necessity. Playback of audio and video presentations is required for all hardware. Because our instruction will be individualized and easily accessed through the Internet, teachers may work from any location. The pace of this course will rely on the user. However, to orient the participants to the course, some sort of introduction/job aide will be necessary.**

==In contrast, the performance environment will take place in a classroom. After conducting an audience survey, we found that the average classroom held approximately 16-20 students. Four out of five classrooms consist of the same grade level, with abilities ranging from proficient to below basic. Student gender population varies from class to class, consisting of an equal balance of boys to girls, or a class with more girls or more boys. There is either a low number or no English Language Learners (ELL) in this environment. Classrooms include most of the following technologies: document cameras, interactive whiteboards, calculators, computers with internet access. ==

Environment....(from AUD) [Consider environment – first the environment in which performance will occur. This is the place where the learning from your product will be applied. Paint a picture of the setting in which the audience is expected to perform. What is this setting like? Are there other people present? Is it a slow, or fast-paced environment? How does the environment impact performance of the intended course outcomes?

Now, consider the training environment. This is going to be technology-based training. How will you orient your audience to the environment in the training itself? Think of ways you can make the two environments match – at least in part.

Note that this is part of defining the // condition // component of a behavioral objective.]

Content (or function)....(from SME) [Use task and subject matter analysis to explore your chosen topic. Present an overview of the course content here. Review your EDTEC 540 content specific to these types of analysis. Consider use of concept maps and outlines to provide a high-level view of the content and how it is organized in the mind of the expert performer.]

Why Write Such A Course? In the survey we conducted, teachers were in agreement that their algebra lessons are generally not very engaging. Respondents said they considered less than 50% of their lessons to be engagaging. Algebra is generally a very difficult subject to present in an exciting manner. 95% of the algebra video presentations available on the market are incredibly boring. They generally are made by simply filming a teacher standing in front of the room lecturing to their class. Prentice Hall is a billion dollar publishing house with algebra textbooks in every district in the nation, yet the lack of creativity and ingenuity in their video presentations, (as well as their textbooks) is unbelievable! (It would almost lead one to think the quality of the product has no bearing on the sales.)

So where does one turn for help? Teachers are also the end-users who bear the brunt of having lessons that are particularly boring. When students are not engaged, not only does student performance suffer, but classroom management also becomes a nightmare. Thus the need for good quality web-based instruction in technology and basic principles of learning theory that would allow teachers to develop their own presentations that will best meet needs in their particular classrooms.

Course Content According to Morrison, Ross, and Kemp, in __Designing Effective Instruction__, (p. 78), " A topic analysis thus provides two types of information. First, it identifies the content that is the focus of the intended instruction. Second, it identifies the structure of the components (Bruner, 1963)."

In "Teaching Algebra in the 21st Century Classroom", we will be presenting algebra instruction from three vantage points: technology, learning theory, and algebra skills/knowledge expertise. The technology aspect will be covered through Kelly Smith, who instructs teachers in the use of technology at San Diego State University, (SDSU). The learning theory aspect will be covered through both Kelly Smith and Ken Miller in our studies of Educational Technology at SDSU. Finally, the algebra skills/knowledge expertise will be covered by Ken Miller and Tom Clark. Ken Miller has taught algebra for six years and has done an extensive study into best teaching methods. Tom Clark taught algebra for thirty years and has written his own algebra course, Videotext Interactive.

The course is designed to help teachers supplement their presentations in the classroom and is not intended in any way to replace the need for a teacher in the classroom. In "Teaching Algebra in the 21st Century Classroom", all the lessons will be aimed at either helping the teacher step back and look at the over all content of the entire lesson, or rethink the way they are presenting individual components.

The technology lessons will be either on the general use of technology in the classroom or how to specifically utilize technology such as:
 * Video instruction
 * Interactive whiteboards
 * Document cameras
 * Presentation software
 * Online instruction
 * Online activities
 * Online games
 * Student response systems ("Clickers")
 * Personal devices (like "iPod Touch")
 * Calculators

For the learning theories part of the instruction, the main focus will be on ways to reduce the Cognitive Load, which can be a major factor when it comes to students not being engaged.

Finally, when it comes to the algebra skills/knowledge aspect, there will be lessons where teachers will be asked to revisit the way algebra has traditionally been taught, reconsidering the order in which the material is presented, along with the methodology in which some of the material is presented. This third aspect will also indirectly be dealing with Cognitive Load and Behaviorist approach as opposed to a more Constructivist approach. For example, there are ways that the algebra curriculum could be taught that would reduce the amount of new information that would be needed in order to master the concept being taught. There are also explanations that could be given that will help algebra make greater sense, such as "when we multiply fractions, why are we instructed just to 'invert and multiply'?" Additionally, by including the historical background of concepts, such as the invention of "zero", students have a greater appreciation and retention of the concepts being taught.


 * Introduction**

It is no secret that one of the most difficult subjects for students to pass is algebra. In fact, in the United States, 50% of all students fail algebra the first time they take it. Former Los Angeles Unified School District Principal Roy Romer said that failing algebra was the main cause for dropping out than any other subject.

There are many things that can be done to improve the passing rates for algebra, but central to all instruction is the lesson which must be delivered in the classroom. Although teachers vary in their expertise, enthusiasm, and delivery, they all must present the same material. Teachers can only do so much to entertain their students, an in the end they must figure out a way to present the materialso their students will listen. So every teacher needs to do everything within their power to make their lessons as engaging as possible.

"Teaching Algebra in the 21st Century Classroom" is a web-based product designed to instruct teachers on how to present engaging algebra lessons. The combination of technology, rethinking about how algebra is traditionally taught combined with an understanding of some basic principles of learning theory can help teachers to not only keep students' attention, but ultimately improve student performance.

The following analysis is a training needs assessment identifying a skills/knowledge problem, the teachers' lack of skills/knowledge essential to making their lessons more engaging. As Allison Rossett has said, "Deciding whether to observe, interview, or survey isn't the hard part. The challenge is to determine sources, plan stages of assessment, and frame questions that will enable a professional to move crisply from a general problem with limp french fries to a series of actions and recommendations that will guarantee yummy ones." One of our goals in this course is to clearly define the problem and clearly address the solution.

Rossett, A. (1995), "Needs Assessment." In:Anglin, G.J. (ed.)(1995). Instructional Technology: Past, Present, and Future. Englewood, CO: Libraries Unlimited.