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.
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