CEP 800 Lesson Plan Reflection

Lesson Summary

My lesson was set up primarily for high school freshmen taking the Algebra 1 Fundamentals class.  I see the lesson as a review of a concept which students should have learned in the 6th and 7th grades.  However, it may have been a first encounter for students with an IEP, who had been in a Resource Room setting for their previous math classes.  The lesson, designed to be somewhat brief, incorporates a short pre-assessment, to get an idea of where students stand with the idea of combining like terms and The Distributive Property.

After taking the pre-assessment, students are to utilize the link given them at the end of class to go online and “independently” view a short lesson on The Distributive Property by the next day.  Upon returning to class, the lesson will be viewed again (hopefully), by the entire class and then discussed.  During this discussion, students are to ask questions and get clarification on any misconceptions they may have related to the concept.  The lesson will be followed by a brief post-assessment, which will be utilized to determine which students may need the most initial support with upcoming concepts.

Lesson Implementation

Not having access to my targeted audience, I thought to access friends and family who may have had some remembrance of Orders of Operations, but were surely removed from their days of combining like terms and The Distributive Property.  Feeling adults would be even more guarded than students, I implemented the lesson individually to each of the three participants, starting with the pre-assessment.  Following the pre-assessment, I gave each a link, which I asked them to view and get back with me the next day.  

My “students” were:

Rich 38, works on the line at Ford Motor Company and hasn’t had a college class in 20 years. Though not intimidated by math, Rich did state that it had been a long time since he had attempted math, but he was a willing participant and gave his best effort on the pretest.  The pre-assessment showed that Rich was confused regarding the difference of an expression and equation.   Rich attempted to solve the expression, rather than simplify it and eliminated the variables, which had not been assigned a value. Without providing any feedback at that time, I gave Rich a link to independently explore The Distributive Property, prior to our next meeting, as I would also do with my other participants.

Jim 42, works custodial at Mott Children’s Hospital who just returned to college for nursing and is taking Pre-Algebra.  Jim is typically very confident and takes things head on.  Additionally, he is taking a course similar to college pre-algebra, so I figured that the combination of the course and his approach to challenges would serve him well.  Though this was the case, I found Jim to be seeking much affirmation during the pre-assessment, commenting aloud as to obstacles he encountered while he went forward.  I had to be careful not to respond, as I did not want to influence his work and negate the pre-assessment.  He did relatively well, as I expected, but did make mistakes in the presence of two variables.  He too was given the link to view independently.

Amy (late 30’s), works as a certified nurse aid at the University of Michigan Hospital and is also taking courses to become a nurse.  Amy also received special education support in math and reading, during high school.  She continues to get various supports in college and has come to me for support with Algebra.  Amy is very gentle-natured and genuine person and was very open about her lack of confidence in attempting the pre-assessment.  However after some reassurance I gave her the pre-assessment, collected it and gave her the link to explore.

Going back through with each participant individually, I had mixed results.  Rich seemed to be grasping the concept, but was going to need more time to really get back on board.  Jim was very confident he could nail it, but still needs to slow down and pay attention to the process.  He would occasionally skip steps and it would hurt him.  Amy on the other hand, benefitted from being able to have the steps in front of her.  

While having a grasp on the concept, Amy still lacked confidence.  She needed to have something in front of her to provide reassurance.  While she stated she liked being able to watch the steps independently, this would not work for her on an independent homework assignment or an assessment allowing notes.  She would constantly be clicking back and forth to find the slides in the video she wanted to reference for guidance and it would take forever.  I afforded her access to the slide show, to view in order.

Reflection

Question Set One

My hopes in teaching a lesson on The Distributive Property, were not about what is being learned, but rather what is being reviewed or “relearned.”  Having observed students being challenged with the concept over the last 15 years, I felt there needed to be some sort of supplement.  I’ve noticed that students have difficulty either applying or remembering The Distributive Property.  Their tendency is to stay hard and true to the concept of Orders of Operations, where they follow the order of first solving anything in parenthesis, then all exponents, followed by multiplication and division (of equal value to each other), and concluding with addition and subtraction (also of equal value to each other).  This works well up until variables are brought in.  Then we have students combining terms which are unlike.  It was because of these observations that I felt it necessary to develop a lesson to reteach or review the concept in the early parts of the, mostly freshmen, Algebra 1 Fundamentals class.  

To move forward, I had to have knowledge of some technologies.  Creation of slides required I used some type of presentation software.  This could be Google Slides, Power Point, or Keynote, to name a few.  Next, I would need to know how record my voice into a software, which I could integrate into those slides.  While I prefer GarageBand, there are other apps out there.  Finally, if I wanted a video, in my case, I needed to be able to operate iMovie.  Put those all together, upload them to YouTube or Vimeo and you’re good.  There is also  the option of just uploading and assigning audio files to individual slides on your presentation software.  While these are my preferences, there are other options out there. 

While I may not experience the same problems with a higher level group of students taking “regular” Algebra, the fundamentals course is set up to go at a slower pace and allow for students who need some variations, accommodation, or even modifications in their instruction.  Knowing this about the course and having helped students with Algebra throughout my 15 years of teaching, I started with three assumptions really.  The first, was that the need to understand The Distributive Property in order to be successful in Algebra wasn’t going away.  The second and most important in designing the lesson, was that students were going to have trouble with the concept.  The third was that the source of trouble, was going to be centered around the students’ tendency to follow Orders of Operations and ignore any exceptions that may come in, related to combining like terms. 

The pre and post assessments give me the best barometer of which students may need extra support or alternate forms of instruction, in addition to the online component.  I will be able to follow up with students and provide additional support as needed.  Though the lesson incorporates technology, the majority of the lesson is based around interaction.  Students only utilize one observation of the video independently, while the continuation of the lesson the next day is intended to allow for interaction both with peers and the teacher, while reviewing the video as a group.  It could be argued that all learning theories are present here. 

Behaviorism is present in multiple forms, as some students may have been conditioned only to apply Orders of Operations, while also taking on the role of the passive receptor.  The hope is that the lesson will take students on a slow progression of each of the theories, moving through the concept of Information Processing next, as the students watch the video and are guided toward a more complete understanding of The Distributive Property.  

The next day, as the group observes the online component together, the teacher will have the opportunity to hear students conceptions as the class works through the slides and discusses the process.  Finally, following the assessment, it is my hope that the students evolve into roles of collaboration in completing their work.  Provided the lesson goes forward as it should, there should be a number of students within the group who are confident, active learners.  These students can contribute positively to the learning of others, as they help to create a social learning environment.  This also frees up the teachers to support students who are having significant challenges.

Question Set Two

The technology component of this lesson is really rather simplistic.  It is in some ways intended to be in the form that students in 2015 access media on an almost daily basis.  It is neither overly light or heavy and allows the students to access it independent of the instructor as well as peers, providing for a self-paced, somewhat personal interaction,.  The only notable disadvantage to the medium being that there is no access to immediate feedback.  With media taking on the form of a temporary instructor here, Cognitive learning theories apply as students are guided toward a more complete understanding of the concept of The Distributive Property, of which most should already be familiar.

CEP 800 Tech-Integrated Lesson

Title of Lesson: Reviewing and Relearning The Distributive Property

Grade Level: 6-9

Length of Lesson: 25-35 minutes

Day 1: 5-15 minutes

Day 2: 15-20 minutes

Context of Lesson: This lesson would take place during first part of a trimester and be introduced at the end in the last 10-15 minutes of a class hour, as a pre-assessment is handed out to the class and a link then given to the class.  Though students have likely been exposed to this concept in previous grades, the targeted population will have demonstrated difficulty with the process of simplifying expressions.  Some middle school Special Ed. students however, may have made a transition from a middle school resource room math to a high school Algebra 1 Fundamentals  type of class.  In this case, they may not be familiar with this concept.

The primary audience for the lesson would be students in Fundamental Algebra courses (probably in 9th grade) and special education students who have had difficulty following proper procedure in math class.  The purpose of the lesson is to ensure the students understand that applying “Orders of Operation,”  to expressions such as 3(5x +2) can cause problems when the terms in the expression are not like terms, as those terms may not be combined through the operations of addition and subtraction.

Materials/Resources:

Paper

Writing utensils

Access to calculating device

Internet access via computer, cell phone, tablet, to view video accessible on YouTube or

teacher website

One of the following: white/chalkboard, overhead projector, document camera, LCD projector

Overview: While the lesson may be a review a to a select group of students, many of the students to this point have displayed a perception that “Order of Operations,” is carried out the same, regardless of expression make up.  For example: Students may believe that 3(5x+2) factors out to be 21x or 15x+2.  Many students also fail to show work and confuse themselves in the process.  Students will likely demonstrate this misconception as they complete the in-class pre-assessments.  Students will then be provided a link to access as an out of class assignment (possibly homework), with the hopes that misconceptions are addressed.  The out of class assignment will then be reviewed in the next class and the

Objectives: Students will be able to identify errors in their work, related to misconceptions they began the lesson with, regarding The Distributive Property and Orders of Operations when the integration of variables takes place and only like terms may be combined.

CCSS.MATH.CONTENT.6.EE.A.2.B

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

CCSS.MATH.CONTENT.6.EE.A.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

CCSS.MATH.CONTENT.7.EE.A.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Essential Questions:

1. Is there more than one way to evaluate an expression?

2. Does Order of Operations (PEMDAS), as it is stated, always lead you to a direct answer?

3. What is The Distributive Property?

4. How does The Distributive Property provide a more accurate outcome, when dealing with variables?

Anticipated Student Conceptions or Challenges to Understanding:

It is anticipated that many of the students will be concrete in their thinking of “Orders of Operations,” applying the rules of (PEMDAS), despite the presence of variables and presenting incorrect outcomes, i.e., 3(5x+2) = 21x or 15x+2.  The challenge here is that students may have missed or need to relearn the concept of combining like terms and The Distributive Property.

Assessment: Students will first be given a short (about 5-10 question) pre-assessment, which will present them with the task of solving various means of multiplying terms through the application of The Distributive Property.  The class will be assessed again, the following day about midway through the class session, after reviewing and discussing the online portion.

Procedure:

1. Introduction- Leaving 10-12 minutes at the end of the class, students will be given a pre-assessment of a concept which will become prevalent in much of the classwork going forward.  Many of the questions will be basic multiplication in various forms, such as 5 x 8, 5(8), (5)(8), to familiarize the students with the concept of using parentheses and numbers in multiplication.  Following these, problems may evolve to place two numbers in parentheses, which are being added.  For example: 5(8+2), 3(5+6).  Finally, variables will be integrated into problems to assess student understanding of combining like terms appropriately.  Problems may present as follows: 5(3x+4), 5(x+y).
2. Following completion of the quizzes, students will be given a link to access outside of class time.  This link will provide a breakdown review of the Distributive Property and its application in the presence of variables.  Students are expected to view this on their own time or access a teacher for assistance doing so, if this is not possible.  Students will be encouraged to email or meet with one of the teachers for support, if they are confused by the online content.
3. The next day, at the beginning of the class period, the class will review the video presentation and discuss The Distributive Property and its application going forward.
4. Closure: Hopefully students have viewed the video at home and the following day in class. After reviewing the video in segments with the class, a short, 7-10 question assessment will be given to the class.  Time allowing, students will begin work applying the concept the have just reviewed.

Accommodations: Students who do not have online access are responsible for working with a teacher or even peers to ensure they access the material prior to the next class period.  Alternate viewing times will be given.  Students unable to access the material due to a disability will be afforded opportunities in accordance with their Individualized Education Plans.  Other students will provided support(s) as needed throughout the class period.

Notes:

Content: The content being taught here covers Orders of Operation as they may relate to The Distributive Property and could be seen as review, if it is being taught at or above the 8th grade level.  Students often inaccurately apply Order of Operations while trying to use The Distributive Property.  The CCSS are more in alignment with those of 6th and 7th grades, but the lesson is meant to supplement and assess student readiness for upcoming work in the course.  Students will be given a pre-assessment to establish where the class is as a whole, with the expectation that a short video lesson will be viewed outside of class, reviewed again by the class the following day, accompanied by class discussion.  

Pedagogy: The lesson will apply the learning theories of Cognitivism and Social Constructivism.  Students will be
requested to access prior knowledge, apply previously learned concepts, and, in some cases, restructure some of
their prior knowledge as they access the “Web 2.0” portion of the lesson, in order to better grasp The Distributive
Property.  These processes will involve student in both the “Information Processing,” and “Cognitive Constructivism learning theories.  The following day, the process becomes more social, as the class discusses the “Web 2.0” assignment and breaks it down as a group, looking for areas of confusion or misconceptions the students had before and have after viewing the online portion of the lesson.  This is where the lesson moves into the Social Constructivist theory, as it becomes group discussion, prior to the follow up assessment.  Going forward, it is expected that some forms of Social Apprenticeship will evolve as students become more comfortable with the
process and are willing to seek guidance from the teacher and their peers.  My hope is that this process will reach
all learners.

Content & Pedagogy: The hope is that the content is a review for much of the class, but in my experience, this is not often the case with an “Algebra 1 Fundamentals” class and it is important to expose the students to the content, while also assessing what it is they know or think they know coming into to the content.  The pre-assessment will give a “ballpark” idea of where the group is in regards to accessing prior learning and any preconceived ideas students have about the concept.  The online lesson should give students a different medium with which to access this concept and also give them a non-threatening means to the concept as well.  Having a visual and auditory means to absorb the material, while also being able to self-pace the material should be beneficial to multiple learning styles.  The following day, the class will have discussion around the lesson and work to address any misconceptions and guide those who are struggling with the general concept in the right direction.  This can serve as an indirect formative assessment, though it will not address every student in the class, as the short end of the lesson assessment is intended to do.

Technology: I actually chose to integrate a few technologies we have already used, while also implementing a “Web 2.0” resource we have already used and one I’ve started to dabble with while working in this class.  While I saw these as technologies for specific uses in the past, I now see them all as relatively content-general.  The technologies I have selected are Keynote, Garageband, and iMovie, to be applied to YouTube.  I chose these, because I would like to improve my skills in using them, but also because they are commonly used, practical, don’t seem overly complex, and all three seem to be available for free use to some scale on various platforms, which would allow me flexibility, should I not have the funding to invest in a website membership or a program in the future.  While these technologies are not vital to my ability to complete the tasks, they should be beneficial in presenting the material in a different format.  

As a Special Education teacher, we are rarely afforded content specific programs.  This is especially the case at the high school level. This method affords me the opportunity to create supplementary material, while catering it directly to both my own and the student needs.  Additionally, I almost looked at this as a lesson I could create in a co-teaching situation, where I am working to support and supplement the material already being taught in the class.

Technology & Pedagogy: The hope is that the online lesson provides a safe, self-paced, visual and auditory learning environment for student.  While there is not a direct application of what is learned through technology, there will be in-class follow up, with application of the social constructivist learning theory.  This will be achieved through the follow up lesson the next day.  The lesson first starts with teacher and student interaction as they work together to evaluate the video and con-construct any missing concepts within the lesson.  From this point, the hope is that students collaborate with and support each other's learning and growth.  Should this material go to a blog, as opposed to just YouTube, students would then be able to post or email questions or concerns privately for feedback related to the online presentation.

Technology & Content: Though the ideas are fundamental, they are a very key part of student success within high school mathematics.  The technology will afford students another means of accessing the content even after they have left the class.  The technology will also take two concepts and show how one may cause confusion in its application of the other.  Additionally, students will be given a demonstration of how to properly show their work (albeit on a smaller scale).  As a whole, across both the Pedagogy and Content aspects, this technology is content-general and should afford teachers the ability to be flexible in editing and refining its presentation over time.  

Assessment: While the assessments will be in class, the online portion of this lesson should afford students the ability to self-assess their understanding of Orders of Operations and The Distributive Property as they go along.  Though the class will be given both a pre-assessment and a post-assessment, student will be assessed formatively as the class progresses, based on their ability to apply the concept of The Distributive Property and show their work, as it relates to individual assignments.

Digital Story

CEP 800 Digital Story

I welcome and appreciate feedback here.  I really wasn't sure where to go with this project at first, but this was a positive experience, which I felt had hints of all the main theories mixed in.  There were rewards for wanted behaviors/habits, preconceived mindsets we had to change, set facts and terms to be skilled and drilled, yet also acquired via collaborative and social means.  The kids learned a new way to study and taught me new ways to interact with the study tool.  Going back through and telling the story, I realized that it was a pretty neat occurrence with a group of kids who really didn't think they were going to be successful in a math class.  I hope everyone enjoys.

CEP 800 Blog Assignment 1 (The Interview)

Blog assignment #1, Interview Podcast

As a Special Educator, this assignment put me in a different, probably best described as uncomfortable situation.  My background is Emotional Impairments, so there is an emphasis on developing relationships with students, knowing about them and what makes them tick.  Along with this, I am a Teacher Consultant, so I spend time working with my colleagues to help them come up with ways to make new concepts and lessons click for the kids.  I do a good deal of adapting and accommodating.  All this being said, I don't have a specific subject matter that I teach or specialize in, because I have to support all curriculum at the high school level in order to help my students pass classes and move forward toward graduation.  Whether it be reading, writing, math, science, foreign language, or vocational classes, I have to do my best to support my students.  
So coming into this, I found myself trying to come up with a topic which I felt as though I spent the most time helping my students with and one which had been somewhat consistent over the course of their academic careers.  The subject I chose was the writing process, though I chose to interview individuals who were out of high school, removed by no more than 3 years.  I also chose to interview students/former students who I knew to be academically confident, at the very least, in the area of writing, in hopes of eliciting a more thorough response.  Only one of the interviews made the cut as one of the students fell ill and the other got stuck out of town.  I found the experience to be enjoyable, albeit tedious while learning the editing software.
By most standards the writing process is about 5 steps, though some sources go into more detail, for all intents and purposes, the following interview(s) will be looking for an "rough" outline of the following:

1. Prewriting
2. Drafting
3. Revising and Editing
4. Rewriting
5. Publishing

Steps provided by ReadWriteThink.org

CEP 800 Podcast Interview- The Writing Process