eJournal 6: Selecting Instructional Media

The selection of the most effective instructional media can make the biggest difference in whether the learner will have the best chance of understanding the concept or content of the lesson.

For the instruction of coordinate geometry, I choose to employ several tools that allow the user to be interactive on the coordinate grid.   Pencil and paper make the process of plotting points and reflecting an arduous task.  While the student needs to know where to place the points and how to graph a set of numbers, too often that process gets in the way of understanding the effects of reflection, translation and rotation.    Geogebra offers the students the ability to visualize the result of a reflection even as the shape is changed through interaction.   The idea of a line of reflection can be introduced or ignored by toggling a checkbox which either shows it or hides it from the grid.  

Questions and instructions can guide the student through a series of discoveries and give the learner a sense of control and freedom in their learning.

LearnAlberta is another tool which provides the students a similar interface and also have videos to help the learner to explore the concepts of coordinate geometry.  The virtual manipulatives  provide them with a visual representation and the ability to move the objects to see how they interact with each other.   The questions are associated with a game which help provide motivation for the students to figure out the correct answer so they can get to a new phase of the activity.

Some of the challenges for using media like this opposed to sticking with pencil and paper, is the range of activities available and the ability to create new, updated content.   Geogebra has a vast selection of worksheets provided by teachers who use the system.   Teachers can read the tutorials and learn how to develop worksheets that may fill gaps identified by their own students or fit better with their districts curriculum.  Learn Alberta seems more static than the other platform, so it will only be as useful as it connects to the need.   Changes to the system will require feedback or requests which may or may not be implemented.

eJournal 5: Identifying Instructional Strategies

The Instructional Strategy

Inquiry based learning will the be strategy employed to teach the coordinate geometry unit.  The following statement from Stephenson provides a solid justification for using this method, "The power of an inquiry-based approach to teaching and learning is its potential to increase intellectual engagement and foster deep understanding through the development of a hands-on, minds-on and ‘research-based disposition’ towards teaching and learning. Inquiry honours the complex, interconnected nature of knowledge construction, striving to provide opportunities for both teachers and students to collaboratively build, test and reflect on their learning."

How will I engage and motivate my learners to learn?

8th grade students like to feel like they are in control or have choice in what affects them.  Providing them a series of choices and responsibility for their learning will allow them to engage instruction without feeling like they are forced.   The choices are carefully calculated and will entail the same amount of work regardless of which path they choose.  

What is it that the students will learn and in what order?

1. Students will be grouped in pairs or threes, and will get to select a topic from a list to introduce to the class.
2. Each topic will have a group activity which might include activities from the following site: Learn Alberta
3. Each group will need to find a real life example of a coordinate grid and how it is used, what units are measured, etc.
4. Several problems will be provided to the students to choose from which involve dilation and scale factors such as: 
1. Find the dimensions required for the purchase of a banner for the front of the school
2. Discover the cheapest way to feed the school pizza from the local pizza place using the cost and dimensions of their pizza pies
5. Find in real life examples of reflections, translations and develop a poster describing the transformations

How will I know that the students have learned the material? And how will I let learners know whether they've learned?

• A rubric for the topic introduction will be provided to gauge student performance as well as other rubrics for the projects and problems selected by the students.
• Exit tickets will be used to test their knowledge for the material explored that day
• District and Campus Check Points will be administered by the math department.
• Using a message board will allow the students to reflect and provide the teacher an opportunity to give personal feedback to each post. 

eJournal 4: Analyzing Instructional Goals

What kinds of thinking do you value and want to promote in your classroom?

There are several kinds of thinking needed to work through the unit of instructions of Coordinate Geometry for 8th grade.  The students have already had exposure to many of the concepts and have experience with the grid.   The new concepts will build on that knowledge and they will be required to analyze the information or problem in parts or by their relationships.

Using Marzano's Thinking Skills Levels I want the students to be able to recognize the patterns and relate them to what has already been taught in previous units or even grades.  The should be able to organize the information in the problem so they can identify patterns that might appear.

I also want them to utilize some critical thinking skills such as developing questions about what they see and to leverage their curiosity to want to find the answer.

Another type of thinking that I want the students to benefit from is reflection.   To contemplate what they learned and what value it might have in their learning or what skill or knowledge did they use from previous learning to advance their understanding of this unit.

The unit provided by the district outlines the TEKS as a categorization of Objectives or Goals.  I believe the following are more goal oriented as it does not provide a specific objective:

1. Geometry and spatial reasoning. The student uses geometry to model and describe the physical world
2. Patterns, relationships, algebraic thinking. The student makes connections among various representations of a numerical relationship. 
3. Geometry and spatial reasoning.The student uses transformational geometry to develop spatial sense.
4. Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. 

I think for the most part those goals are helpful, but I would also add the following: 

• Develop a better understanding of the vocabulary for coordinate planes and mathematical operations
• Recognize and apply various representations of equations to aid in problem solving
• Organize mathematical writing as a strategy for solving problems.
• Reflect on prior learning and how it affected the current unit
• Develop questions and predict possible solutions or answers 

eJournal 3 Analyzing Learners

This goal this week is to further analyze the learners for my instructional design.   The scope to consider for students stretch further than their performance in the topic or supporting skills.  To make better instruction, it is well worth the effort to recognize characteristics that make up the learner and to understand how they affect their ability to learn.

Student population data

Reviewing the enrollment statistics for the state of Texas, it seems half of the student population are economically disadvantaged.   The school that will benefit from my design is a Title 1 school which implies that a majority of the students are on free or reduced lunch plans.  Being disadvantaged economically might have implications of lacking supplies to come to school, or the ability to venture outside of the area to learn about how other people live.  The lack of broad experiences would affect their ability to make connections with the content provided in the lesson.   Parents are not as likely to have higher education backgrounds and may not value education and therefore support the students efforts or hold them accountable.   The ability to bring the student to school for extra tutoring or allow them to stay late and arrange transportation may be a challenge as well.

Another statistic is the number of Hispanic learners in K-12 which also accounts for more than half of the population. Some implications of this statistic could be that parents may not have the language skills to understand the instructions.   Parent / Teacher communication is key to student success and language barriers might keep the parent from partnering with the teacher to support their student's learning.    A interesting metric is the Limited English Proficiency percentage which is 15% of the population.   Considering the difference with the number of Hispanics and other ethnic groups, it seems that the students do not typically language as a barrier.

This information was taken from the TEA web site: http://www.tea.state.tx.us/acctres/enroll_index.html, 2011-12 enrollment report

Characteristics of students

Other characteristics of my learners come from a comparison of child learner and adult learner.  Here are some of the highlights of the report.

• Children are not self sufficient, they look to adults for material, psychological support as well as life management
• They may perceive one of their major roles to be a learner (although it might not always be accepted)
• They learn what they are told and I believe they typically expect to be told everything 
• The grade levels are grouped with the same ages and typically experiences with some variation
• They have limited experience
• They can learn quickly
• They are open to new information and able to adjust their views
• Often externally motivated with rewards, praise, recognition
• Their expectations are typically limited in regard to education as their experience is small
• They are still developing their brain and need time and opportunity to make connections 

The report also discussed needs of the learner much along the lings of Maslows hierarchy of needs.  Children are more likely to have some of these needs unmet at the lower levels which will distract them or prevent them from focusing on education and contributing in a positive way to their learning.

This information was taken from:
http://www.itma.vt.edu/modules/spring11/efund/lesson3/learneranalysis.pdf

My personal observations from the classroom.

They may or may not recognize the importance of a positive attitude and how that affects their ability to learn.  Nor do they recognize how that attitude can affect other students (their learning partners).  The concept of being a responsible learner is not typically understood by the middle school student.  Understanding what type of learner and how to adapt to other forms of information is not readily known by the student.   Reflection may or may not be something that they are familiar with.

Middle school students are beginning to branch out socially and are starting to learn the rules of engagement as it relates to peers and the opposite sex.   They can be competitive and their desire to rise to the top of their environment can keep them from seeing the value of cooperation or team work.

They do not want to be embarrassed or thought of as not knowing something that others already know.  The idea of failure is not comfortable and avoiding questions seem to be a coping mechanism employed by many of the students.

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.