The "Connections to Algebra" unit plan was created as an attempt to infuse standard math teaching methodology, observed in roughly a dozen different classrooms by the author, with some new teaching techniques that will better address the needs of today's math students. In particular, the primary goal for the unit plan was to improve support for the following:
The features that were included in the unit plan to meet these goals were:
Each of these unit plan features are discusses in detail below, with emphasis on how these features were intended to help meet the goals described above. However, before getting into lesson plan details, let's take a moment to discuss why the particular stated goals are so important in today's teaching environment.
Today's teaching environment presents a number of challenges which need to be addressed by any new teacher who wants to provide the best possible support for today's student base:
Based on data from the 2002
California English Language Development Test (CELDT), EL students
comprise 24% of all California students. Even in 12th grade,
by which time many EL students have either dropped out or been
reclassified as Fluent English Proficient (FEP), EL students still
account for 10% of the overall student population. While the
bulk of these students are rated level 3 capable or above, even these
higher rated EL students will typically have problems with
academic language, and may be slower picking up data from verbal
lectures - even though their conversational English may be more than
adequate.
It has always been the case that students learn at different rates. However, today's math teacher is likely to face a much broader range of student abilities simply because the minimum standard for math graduation requirements have been raised, and now every graduating high school student must pass through at least algebra I. So, students that may have stopped at pre-algebra or who may have opted for business math in the past, now must continue on to more abstract math. This makes it more important then ever for teachers to be able to support slower students while not leaving the quicker students to fester in boredom.
The plain fact of the matter is that many of today's students do not do much, if any, homework. Often this is a result of lack of pressure at home from parents who do not have time to supervise their high school age children or who lack a background in academic success as a basis for knowing how to enforce good homework habits. Other times this is a result of students having parents who do not understand English, so they are unable to assist their children in their assignments. Moreover, even among parents who are motivated and who understand the language, few have the personal background in math needed to be a significant help at home in higher math classes such as algebra. Therefore, it is important to give students a chance to accomplish as much as possible during class time, and not assume that they will get support for homework outside of class.
The "Connections to Algebra" unit plan has a number of features designed to address the goals stated above so as to successfully educate as many of today's students as possible:
The "Connections to Algebra" unit plan provides the following features to promote a collaborative learning environment:
Seating Arrangement: For the majority of classes, the students are placed in four person learning groups, with two desks placed side by side butted up against two facing desks that are also side by side. This makes it easy for students to work together on guided practice and in-class homework time, which in general will take up the bulk of class time.
Group Work: In general, guided practice will be attempted in the four person learning groups on a shared portable white board, while the notes generated as a result of the guided practice will be taken by each student. Also, some homework examples (especially in the final review) will be presented by the learning groups to the classroom.
Enhanced Teacher Mobility: By putting the bulk of the instructor presentation material on PowerPoint slides controlled using a PC remote, the instructor will be able to do the bulk of the instruction from different points in the room. This will enable the instructor to join in with students on working the problems and to get immediate feedback on students' progress.
The advantages to a collaborative working environment with respect to the above stated goals are as follows:
EL Students: EL students sometimes have a harder time than most instantly understanding the academic language used in algebra lectures. By working in groups, these students have a chance to pick up what they may have missed from the other students in their group. This effect actually benefits all students, since every student occasionally fails to pick up some piece of information that their fellow student may have caught. However, EL students are especially likely to benefit.
Differentiated Learning: Group collaboration gives some students the chance to pick up a tutor role and pull up fellow students who may be having a harder time coming up to speed. This actually benefits both the tutor and the tutored student, since tutoring a subject can be very helpful in mastering it.
Other Benefits: One of the greatest benefits to collaborative learning is the reinforcement that working together can give to the learning process. In the process of explaining things to each other and arguing over approaches, students gain additional insights into the mathematical techniques and solidify the meanings of the concepts in their minds. Additionally, collaboration work gives students a chance to work on social skills and learn how to work problems as a group - a benefit which extends well beyond the domain of mathematics.
The lesson plans inside the "Introduction to Algebra" unit plan are built around PowerPoint slides which use dynamic animation to illustrate how and why the mathematical operations are carried out. This includes animation like circling the part of the equation to be changed next, and added text at each step to explain why the step is carried out. The benefits to this kind of approach are as follows:
EL Students: If an EL student doesn't follow what the teacher is saying verbally, she also has a chance to understand the subject matter by simply looking at what is going on on the screen. This can be helpful to all students, but is especially likely to be helpful to EL students.
Engaging Multiple Senses: Learning theory indicates that students learn better if multiple senses are engaged at once. The slide animation helps engage the student visually while the instructor explains the subject matter verbally. This reinforces the learning and gives the student a better chance of understanding and remembering.
[Note: Generating
these PowerPoint slides is a time intensive process, and so brand new
slides were only generated for one lesson. Other lessons
include slides from other sources which can be used for the lesson
plans within the unit, and are intended as representative examples of
external sources for filling this requirement.]
If students lack a supportive environment at home for doing homework, then the homework they get done in class may be the only math work that they do - and it is almost impossible to successfully learn math without spending time doing it. This is why all of the lessons in the "Introduction to Algebra" unit are planned for extensive in-class work, including guided practice and time at the end of class for doing homework in class. This gives the students a chance to do at least some homework in an environment where they can get help from the instructor and from fellow students - even if they won't have time in class to do all homework.
The Power Point slides are part of the strategy for maximizing in class work time by reducing the time spent by the teacher to generate the same information up on the white board or on the overhead projector for each class period.
To keep all of this in-class homework time productive (rather than just having it degrade into a "social hour" for the students), the unit plan incorporates several classroom management techniques aimed at keeping the students focused while allowing the type of open environment that encourages participation:
Class Participation Rubric: The class grading scheme offers the students incentives to participate in class by providing "participation points" as a supplement to regular homework. So, points can be awarded for activities like doing a homework example in class, participating in group activities, and tutoring a fellow student.
Group Pressure: Some of the group assignments are structured as a motivational tool. For example, many of the guided practice problems are designed around trading roles within the group so that each member of the group is responsible for presenting at least one problem solution. This gives that member responsibility for the result of the entire 4 person group, which provides a motivation for paying attention and getting the problem right. On the other hand, members of the group will have a motive to assist the presenter since his result represents them.
Also, some of the multi-step problems are set up so that different members of the group do different steps of the problem. This gives everyone an incentive to see that the other members of the group are doing their part.
Instructor Proximity:
Use of PowerPoint slides and a PC remote allow the teacher the "work
the room" during class. This gives the instructor a better
platform for controlling the class than running the class from next to
the white board or the overhead projector, far away from the majority
of the students.
The standard math textbook used in the unit plan aligns with the California math standards, so a student's mastery of material in the text is a direct reflection of how she is doing with respect to the standards. In fact, this textbook even includes some multiple choice questions to more closely emulate what students typically see on a California standards test (my textbooks of 20 years ago didn't have these kinds of questions). Thus while they are learning to take the tests from the textbook they are also learning to take the standardized test.
Additionally, continuous assessment in class via class participation and homework gives the instructor an opportunity to adjust for any problems the students may be having learning the material, whether that problem is due to English language difficulties, different learning needs, or whatever. The "Introduction to Algebra" unit plan uses a number of methods to maintain continuous assessment of student progress:
Class Participation: Since class participation is structured into the lessons, this gives the instructor real time feedback on how well the students are absorbing the material of the day. The fact that the class participation rubrics add incentive to participate helps assure that the instructor is assessing a serious attempt from the students, rather than a half hearted response which is typical of students who have no incentive to participate in class outside of doing their own homework.
Homework:
As with standard math classes, the instructor will have a chance to
review homework on a regular basis to assess student
progress and areas where the students are having
difficulties.
This assessment can be rather late as far as the
original lesson covering the subject in question is concerned, but it
can be a very important cue to
structuring the final chapter review where all lesson material will be
re-covered.
Chapter Review:
The instructor can take the assessment data collected during
work on the chapter, and use this data over a two class lesson to focus
in
on areas where students are having trouble. Since this lesson
is
designed with a high degree of
class participation, the instructor will have one last opportunity to
assess student readiness prior to the relatively high stakes chapter
test.
Chapter Test: The chapter test will form the main basis for a student's grade at the end of the unit. This test is generated via software supplied with the textbook, which allows the test to have random differences from prior tests or tests given in other classes (to reduce cheating). The author has a high degree of confidence in the quality of this assessment and its alignment to California standards.
The partially completed "Introduction to Algebra" unit plan was not intended to be written in stone. In fact, it was intended as a baseline to work from when developing the complete lesson plan preceding the actual teaching of a class - which in turn would almost certainly need adjustment during the teaching of the unit itself. However, this unit plan does represent the first cut at a particular personal teaching style which is intended to address the needs of today's students using the particular strengths of the author (for instance, his ability to communicate through technology). The final arbiter of the quality of the plan will be the performance of the author's future students.