POGIL Conference – Portland, OR – July 27-29

As part of a KSTF Professional Development Grant, I was able to attend the Northwest Regional Conference for POGIL (Process Oriented Guided Inquiry Learning). In an effort to meet my obligations for the grant, I will post the implementation plan approved as part of the grant and then comment on the outcomes for those specific action items. In this commentary, I will provide the learning from the conference and links to tools learned along the way.

June – July

Read for about 2 hours different published POGIL activities from math or science disciplines to see their successes, challenges and recommendations for improving POGIL in the classroom. Additionally, I will collect and review my previously created POGIL-like activities to compare my lessons with those created using the POGIL process. Conduct an internet search of leading questions (or directives) that could be used in the classroom environment to extract deeper responses from students (such as “can you tell me more about that?”) and make a list. Throughout the implementation of this plan, I will refine this list as I find what is and isn’t appropriate to foster learning.

Results:

July KSTF Meeting

Talk with other KSTF fellows about their practice of group activities, particularly science teacher who have lab classes. Since POGIL activities are similar to the group work and inquiry of a science lab, experienced science teacher may have tools for asking questions of students that lead to critical thinking in the inquiry activity. I am looking for questioning strategies when other teachers are working with groups.

Results:

July 27-29 (POGIL Conference)

Attend POGIL Workshop: Portland, OR. – I will begin on the Introductory Track for the workshop since I have no formal experience with POGIL. During the workshop, I will learn about the process and structure of the POGIL activity, list student learning outcomes from a POGIL activity and create plans for implementation of POGIL in my classroom. POGIL implementation includes facilitation tools for teachers that include questioning and keeping students engaged. I will use this learning for facilitation questioning to refine my bank of questions. Additionally, I will attend workshops about the Activity Structure of a POGIL (creating a framework for learning) and Writing Learning Objectives for the activities.

Results:

August – December

Create a clear classroom procedure for students to teach them how to positively engage in group, inquiry learning. I will Implement this procedure for my Algebra and Geometry classes in the fall when using group work. Additionally, I will create a POGIL lesson for my classroom and I will share out with other staff members to increase success in their classroom. In creating these activities, I would like to work with an instructional coach (provided by the school district) or a colleague to ensure effectiveness. Finally, I will continue to incorporate open ended questions (probing and clarifying questions otherwise known as socratic questioning) during my regular teacher to help extract deeper, more thoughtful responses to my students.

Results:

P2 – Differentiated Instruction

P2 – Practice differentiated instruction. This means that teachers use a variety of instructional strategies or personalized instruction to help students acquire knowledge. Teachers will create opportunities for students to learn the same standards in different forms or with small modifications to fit the students’ needs.

The evidence is a series of mini-lessons presented over three days of instruction as outlined by a previous blog post found here. (LINK TO OTHER POST CLICK HERE) This post also includes some background information about the project, goals and outcomes. These lessons used student activities to help students to learn about and become familiar with vertical asymptotes, horizontal asymptotes, x- and y-intercepts and holes in a graph. Rather than providing students with direct instruction, the activities are built to facilitate student discussion around the topics and the teacher can target students with special learning needs during the activity. Each group was strategically selected to include students who brought different strengths (such as good communicator, critical thinkers in a single group). Group roles were assigned to draw out strengths or compensate for weaknesses of individual groups (quiet students were assigned as readers, critical thinkers assigned to questioner role).

Lessons 1 through 4 use student’s prior knowledge of polynomial functions to build on new understandings. Stations which revolved around asymptotes had students use limits by completing a table of values. For horizontal asymptotes, the values approached infinity and negative infinity. For Vertical asymptotes, the values approached a fixed value of x. Structuring groups with specific roles, students were able to converse and think critically about each of the four topics. Since the conversations were NOT teacher lead, students could explain to each other concepts they were unsure of. Most importantly, I would circulate the room during the activity to check on students progress and assess needs or misunderstandings with groups of about 4 students. I would target groups that were working fast to ensure they understood the intricacies of the activity and would provide challenge or extending information to groups who were able to build on more complex ideas.

After completing this activity, I learned that station learning can be valuable but should be thought through carefully. I would reconsider several processes to make this better.

  1. Allow more time for students to complete the activities. Some groups seemed rushed and were not able to complete ideas.
  2. Debrief with groups after each activity to ensure students understood the purpose of each question.
  3. Provide a little bit of direct instruction before turning to station learning activity to motivate the learning more.
  4. Remove the unit about holes since it is not a standard, but a good to know topic.
  5. I would remove the idea of making the students physically move around the room during the activity, this wasted time.

There are some pieces of learning that I thought were beneficial to the activity.

  1. Assigning students to groups to ensure there are a variety of learners in each group of learning.
  2. Assigning group roles to draw out strengths of students to benefit others in the group.
  3. Circulating the room to provide direct instruction as needed rather than lecturing at the front of the room. The dynamic of a teacher roaming helps students by providing small group instruction AND if the teacher is unavailable, groups must work together to problem solve before asking for assistance and receiving help. The delayed gratification is more effective because students are more receptive to the learning (Meyer, 2010).

While many of the suggestions above would help students learn and are keys to improving the instruction better for next time, I can continue to improve by learning and practicing differentiated instruction and providing alternate means of learning to students when station activities are not being used, such as times when direct instruction is used more. There is more research and practice that can be learned.

References: Meyer, D. (Speaker) (2010, March 1). Math class needs a makeover. TEDxNYED. Lecture conducted from TED Conferences, LLC, New York City.

HOPE Reflection P4 – Technology

P4 – Practice the integration of appropriate technology with instruction. This means that the teacher is actively using the tools within the classroom to extend student knowledge. The technology used may not be the most modern or advanced, but it must be accessible for students in the future and commonly used within STEM fields. Since the students at my school are highly interested in Math, Science and Technology, the utility of this skill is for engineering tasks and aviation are highly relevant to the task.

The evidence presented is a lesson plan that integrates the use of a graphing calculator to solve for unknown coefficients of a polynomial when given a set of points. Even advanced technology and regression techniques in computers cannot solve for a polynomial that is greater than degree 5 without significant  algebra manipulation. Students are confronted with this realization and are directed to create a system of linear equations and are guided to use prior knowledge of matrix operations to solve for the polynomial coefficients. After the lesson plan, there is a set of reflection questions for the teacher and responses which help justify many of the decisions made throughout the lesson. In this commentary I explain the benefit of using a graphing calculator (as opposed to any other form of technology) to help students make connections form mathematical concepts.

Technology Lesson Plan and Reflection Questions

The technology lesson plan meets the program standard because it differentiates for different groups of learners and their experience with a graphing calculator. This tool is most appropriate because ALL STUDENTS have a Texas Instruments graphing calculator (or may borrow one from the class set). Additionally, the use of this type of technology is relevant to students who will continue into college when solving systems of equations are important. To relate this to student learning, many engineer students or those interested in design must learn how to create a polynomial function to fit points on a line. Some students in my class are also taking a class in engineering when they use CAD computer design. The computer automates the mathematical process and this lesson connects the computer process to the math behind the computer.

In creating this lesson, I was able to be highly reflective of the lesson that I was designing. During my internship, I am continuously working to differentiate instruction. In creating this lesson, I was able to challenge advanced students and also support students with another piece of material to help them grasp the mathematical procedure. If I were to do this activity again, I would want to show students another type of technology to accomplish the same task, such as a computer programming language or other online tool. Another way I would like to change this activity would be to have less direct instruction and create a more engaging lesson that would lead students to arrive at the conclusion that matrix operations would be the solution to the problem encountered within the lesson (not being able to model a fifth order polynomial with calculator regression).

Station Learning Activity – Asymptotes

I wanted to try a station learning activity that was inquiry based. Too often asymptotes are taught to students without much consideration for how or why the functions behave in this particular way. Personally, I think asymptotes are interesting, but to students they are a strange phenomena that have no application. The approach with the inquiry is to help students find interest in an abstract learning segment. This lesson comes near the end of a unit about polynomials and we have just covered polynomial long division. This activity is geared to help students learn through the various aspects of polynomial division and what could happen. Since slant asymptotes are unique, we will cover these the next day of class.

Pre-Lesson:

Students have been studying polynomials for about a month and we are just exiting a section about the Fundamental Theorem of Algebra and complex roots. It is clear that students are weak in factoring polynomials, but I cannot afford to stop all learning to generate mastery. So, I have designed a 2.5 day mini-unit in which students will have lots of practice in factoring polynomials, reviewing polynomial division while exploring asymptotic functions. This mini-unit will hopefully tie a lot of somewhat random ideas together and help loop some previous learning so that students can practice skills they should already know and continue to learn new ideas.

On my website (link below, date Feb. 24) I have posted 4 worksheet activities for the day (I created these by the way). As students walk in, they will be divided into 1 of 4 groups. They will read start the entry task which should require them to access prior knowledge. Students will have about 30 minutes at each station to complete a short worksheet. Since the period is 100 minutes long, I expect that all students will get through about 3 stations.

I will be walking around to each group during the class to ensure students are grasping the important concepts at each station and catching some misconceptions along the way.

My personal goal in creating this station learning activity is to: 1) Get students moving in the classroom during a long period. 2) Engage student in an exploratory, inquiry based activity. 3) Differentiate instruction so that struggling students can achieve new skills. 4) Fold in prior learning (factoring, finding roots, polynomial division) so we can move forward in content and review prior knowledge.

http://www.mrgermanis.com/precalculus/3PolynomialModels/index.html

 

2/24
(Block Day)
Entry TaskFor the function f(x) = (x + 2) ÷ (x – 1), describe as many of the following features as possible. DO NOT GRAPH!

  • x-intercept
  • y-intercept
  • end behavior of f (x) as x approaches positive infinity.
  • end behavior of f (x) as x approaches negative infinity.
  • function behavior when the input is close to 1.
Activity“Be Rational!” (Station Learning Activity)

See THESE notes to clarify information from stations.

Journal Reflection: Complete the JR for each associated station you visited today. Build a rational polynomial that:

  1. Has a hole at x = -10
  2. Has a horizontal asymptote at y = -5
  3. Has a vertical asymptote at x = 3
  4. Intersects the x-axis at (3, 0) and the y-axis at (0, -5)
HomeworkThis homework is due on 3/2.
Note: Some problems may cover concepts NOT at your station. During class, we will continue the activity. All problems should be solvable by the due date.Pg. 229-233 # 1, 2, 3, 4a, 7

Lesson Goals: Students will learn about basic asymptotic behavior that results from polynomial division including domain and range of asymptotic functions. Additionally, students will recognize a polynomial which results in a curve with a hole.

Post-Lesson Reflection

My lesson today went well! There are a lot of opportunities to observe students understanding (or not understanding) the ideas of the lesson. I noticed some problems in the wording of some of my activities which was challenging since I needed to talk individually with each group to clarify my writing.

I created groups of 4-5 students and strategically selected different ability levels in each group. Roles per group were also assigned to bring out the qualities of each student that I needed. For instance one group contained a student who generally asks good questions in class and another student who generally has a difficult time engaging in lessons and a third student who has a difficult time asking questions. In this group, I assigned the unengaged student the role of reader, the curious students the role of checker/questioner and the quiet student an arbitrary roll. With these students and roles in the group the quiet student and the unengaged student became members of a group and engaged in the lesson well attaining significant new knowledge. Overall, this strategy worked very well, only one group of higher level students complained about the group roles and didn’t follow the structure. As a result this group was unsatisfied and felt lost during critical parts of the activity.

Thinking about pacing, I am realizing that these activities require a lot of thinking and within a single 100 minute period, students may have a difficult time accomplishing even just three of these activities (the intent was for students to complete 3 of the 4 lessons). If I were to do this activity again, I would divide the problem into two days of station learning and have only two worksheets per day (even during a block day). This will allow me to debrief more quickly to ensure students are getting at the heart and the objective of each station.

Additionally, if I do this activity in the future, I will provide check in point where the document controller will report their groups finding to the teacher to ensure connections are being made and the objective is being met.

One task that should be shared with the teacher in particular are the generalizations of the findings of the activity. Many parts of the activity were examples where students were to uncover HOW asymptotes, holes or intercepts worked. Making generalizations will solidify these ideas and prepare students to apply this knowledge to new situations.