eJournal 2: Analyzing Problems, Analyzing Context

I modified my 5 whys from last week and focus on the student perspective.   Here is the updated 5 why exercise:

The project that I intend to work on is a 8th grade math unit on multiple representations of functions.

1. Why? This is a difficult unit requires the students to shift between the different representations and utilize their knowledge and understanding of word problems, expression building, graphing and deciphering a pattern from a table of data to answer the questions. 
2. Why? Students do not have a firm grasp of several of the representations.
3. Why? They tend to follow along with the lessons but may not take on the challenge of practice or developing their own methods of solving. 
4. Why? Teachers might tend to lecture or spend too much time showing them the method rather than let them get more time experiencing the problems.
5. Why? Students do not fully engage the teacher or lesson and generate questions or develop a confidence that they know the lesson.

Performance Analysis

It is common for students to struggle with the multiple representation unit.  The underlying issue based on the 5 whys is that they may not engage the learning process when learning each of the 4 representations that are taught independently.  This type of unit is type of capstone to functions and they lack a solid foundation or confidence with the knowledge they do possess for each of the components.   The issue is certainly instructional and can be addressed by developing an engaging unit that entices the student to engage a real life problem that is meaningful to 8th graders.  The solution is quite simple, right?


Needs Assessment

The more challenging aspects of multiple representations are graphing the expression or deriving the expression from the graph.   There are fundamental algebra aspects to this problem, but they are not taught slope and offsets until the following year.  Therefore, they have to arrive to the answer through observation.  If they are given the correct type of problems, guiding questions and time to explore and discover the patterns, they should be able to relate the graph to the equation and subsequently to the table and word problem.


Context Analysis

The class size is up to 20-25 students and they are in class for a 50 minute period. They have access to laptops and ipads.   Individual work, pairs and groups can be formed, however, my experience is that many students do not fully understand how to take full advantage of their peers and they get distracted or do not seek help when they do not know what to do or if they have a conflict.  Technology is encouraged by the administrator, however, a student centered, engaged, non-worksheet style of lesson is the only hard requirement by the principal.  The internet at the school sometimes goes out and laptops often requires several minutes to log into the network.    Teachers also like to take lessons and make them their own. If there are parts of the lesson that are critical, it is likely they will respect that part it and leave it intact.

eJournal 1: Project Description, 5 Whys exercise

1. The project that I intend to work on is a 8th grade math unit on multiple representations of functions.  The district provides teachers with a set of stock material to teach the unit and it is up to the teacher to decide the delivery process for the information for their students.  This difficult unit requires the students to shift between the different representations and utilize their knowledge and understanding of word problems, expression building, graphing and deciphering a pattern from a table of data to answer the questions.
2. The challenge for the student is that this unit is a culmination of what they have learned and requires application and analysis which is higher order thinking.   The challenge for the teacher is to find the balance of scaffolding vs. allowing them to struggle through the process of finding the different representations of a function.  The activities and work that the teacher provides need to help the students to learn to reason to find the answers.
3. From the students perspective, it doesn't seem they have a firm enough grasp of each of the 4 representations and how to manipulate the various forms to have the confidence to tackle the challenge.   From the teachers perspective, there might be some timing issues where they are not able to extend or reinforce the underlying skills necessary to solve the problems on their own.
4. The students grasp of graphing, word problems and deriving equations or rules from tables could be better if they were to utilize their time in class better and have a better attitude toward the problem solving.  Often homework is not completed or even assigned for those that need additional practice.    Teachers might be taking too much of the "teaching" burden rather than shifting the responsibility to the student and providing a lesson that is interesting and engaging so that the students want to learn.
5. Creating these types of lessons from scratch for each of the units in a typical year can be overwhelming to a teacher.  I imagine teachers take the material in euphoria, look for interesting ways to present it.  However they have to live with limitations of their own knowledge, understanding as well as time.   They might also lack the ability to adapt what other teachers might offer to their current environment.

The 5 whys technique is helpful in that it helps document a thought process and forces me to articulate what the problem is and dig deeper into why that is a problem.  It is impossible to do this in my head.   If I try to process this in my mind, I can get about 2 levels down, but my mind wanders and I loose track of the major points.   The key for me is to just start typing and work through the process.   The steps and justifications can be edited as I go forward and consider more accurate "whys".

In some ways my scope has broadened because this particular unit relies on the students basic skills with each of the representations. How they are taught from day 1 affects this particular lesson and that is a place that I certainly did not consider prior to this exercise.   It also helped me realize the value of student responsibility and engagement in the process so that I would consider that when looking at the amount of time allotted to teaching this and previous lessons.