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:

M3 bPortfolio Reflection – STEM Research

My ideas of STEM have changed slightly, but significantly since beginning the course. I have learned about the different models of STEM (Henrikson, 2015):

  • SteM – Science and Math are the “bookends” and most important
  • STEM – Integrated focus for both math and science – T&E are integrated and focused on contend and application
  • S | T | E | M – each discipline stands on its own
  • s(TE)m – increased focus on CTE classes that help prepare for selected careers in science, math, technology an engineering.

The best model according to Lantz (2009) is that STEM should be well integrated into the curriculum and that teachers should be collaborating to create cohesive units of instruction that help students learn about all topics together. One tool for accomplishing a truly effective STEM model that was discussed in our class discussions was common planning time across disciplines to help teach similar concepts in different classes. Verlaine (discussion post in Module 2) shared her collaborative approach within her school district, a push for cross curricular teaching. Additionally, Verlaine supported her claims of this effectiveness of teaching similar subject by citing psychological research (Medina, 2008) for increasing long-term memory by repeating information multiple times, within a short period of time using different modalities.

Wiliams (2011) discusses how the use of questioning is important for teachers to formatively asses student understanding to inform next steps in teaching. I assume he would support the STEM model, where each element has an equal share of a given lesson. This assumption is based on his desire to ask inquiry questions such as, “What do you notice?” Earlier this year, I was introduced to an NCTM lesson called “The Hexagon Train Task.” I was part of a group of math and science teachers, we were given four yellow plastic hexagons and asked to line them up “end to end” where a long side would touch another. We were then asked to ]reflect on what we noticed about the aligned hexagons. Some mentioned the color, some discussed the perimeter, others discussed the shape, but overall our ideas were broadened to to accept the next question because of our ability to think abstractly was opened. Soon after, we were asked to think about perimeter and how this could be calculated for longer “trains.” We were just told the purpose of the activity (only slightly though, but the instructor had a clear academic purpose for the lesson, sequences). Having the opportunity to think generally before getting specific allowed both the math and the science people around the table consider a question without fear of being incorrect. Sometimes I struggle with IRE (Initiate, Response, Evaluate) which is off putting to many students, I think I can incorporate more of this open discussion and individual reflection into my lessons this coming year.

Some of our discussions in Module 2 & 3 were about purpose with instruction. STEM cannot be accomplished without clear purpose. Provided that many of us took a methods course about Understanding by Design by Wiggins & McTighe (2005) which stated the purpose of the lesson should drive the activities and goals should establish each lesson (rather than the other way around). This method (backwards design), is at the heart of educational research and is supported by Williams (2011, p. 61). In our class discussions for Module 3 about Project/Problem Based Learning, comments arose about the intent of the learning, rather than the activity itself. Lura’s post about the Rube Goldberg Machine commented on her investigation of PBL activities found on the internet. She mentioned, “Many so-called ‘STEM’ lessons that I did find weren’t anything new, just standard math or science lessons with some videos added about applications” I think this is part of the challenge with PBL is that the purpose should be the beginning of the project, not the act of completing a project, making a presentation or doing STEM. The purpose should be to meet educational standards where multiple modalities should be used to approach concepts. Projects could include multiple standards from a variety of subjects, but that’s not necessary.

Overall, I have learned that STEM should be well integrated. To accomplish this, teachers from different subjects need to work together and students need to work in collaborative groups facilitated by a teacher. The planning can be though common planning time (which is becoming more typical in schools) or it could be through another framework of providing collaborative work time for teachers. Lessons should be revised and adjusted based on formative feedback and through a teachers understanding of unique students needs. Finally, when planning projects, there is a general consensus (although not by all) that the purpose should come first and activities should support the learning of those targets.

Sources:

Henrikson, R. (Lecturer) (2015, June 22). Module 2 What is STEM. EDU6978 Module 2 Course Lecture. Lecture conducted from , Seattle, WA.

Lantz Jr, H.B. (2009). Science, technology, engineering and mathematics (STEM) education. What form? What function. Baltimore, MD:  Report, CurrTech Integrations.

Medina, J. (2008). Brain rules. Seattle, WA: Pear Press.

Wiggins, G. & McTighe, J. (2005). Understanding by design. (Expanded 2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Wiliam, D. (2011).  Embedded formative assessment.  Bloomington, IN:  Solution Tree.

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.

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.

 

Northwest Mathematics Conference (NWMC) 2014

The Northwest Mathematics Conference (NWMC) is a gathering of educational professionals who teach math or provide assistance to math instructors. The purpose if for attendees to gain valuable knowledge around how to teach and learn the latest and greatest instructional tools for math classrooms. All grades and topics were covered, some general educational techniques and others were specific to integrating Common Cores State Standards (CCSS) or other instructional tools into the classroom.

 

Day 1 – Friday

NWMC Day 1

The linked document are the notes I took on day one of the math conference. These only include a little bit about the sessions and workshops I personally attended, however I obtained many resources throughout the conference and this document include many many references to learning tools.

I will copy the session/workshop title and description and follow up with a few vital learning points.

Marc Garneau & Chris Hunter
(Education Services, Surrey School District — piman314g@gmail.com)

I See It: The Power of Visualization

IMG_0918What does it mean to “see” the math? We’ll explore tasks that can engage students to reason and make sense of mathematical concepts through visual representations. The nature of these tasks will include concrete patterning, dynamic
graphing, geometric representation, and more.

The session with Mark and Chris taught us about visualization of mathematical concepts, this followed the Dan Meyer’s model for presenting information and creating debate. One of the most interesting pieces of their workshop was the visualization of square roots. Investigating the fundamental ideas behind square roots would help students understand how to simplify square roots. Squares have the same length on each side and a square root is the length of one side of the square. Participants were provided with a packet of multiple activities that helped students visualize math concepts.

 

Amy Utecht
(Franklin Pierce High School — autecht@fpschools.org)

Algebra Interactive Notebooks

Come discover the world of Interactive Notebooks. I spent the last year researching and creating interactive notebooks to use with my algebra students. These notebooks include notes, foldables, examples, and journaling. I will share resources that I discovered and we will create several pages that were highly effective with my students.

Amy’s presentation of her Interactive Student Notebooks (ISN) was the highlight of today’s workshops. She provided examples of how she supplemented her school’s textbook with activities to engage students and provide an organization to class notes. Students participated in classroom activities and pasted Foldable’s, worksheets and investigations into her notebook. The students essentially create their own textbook by participating in class every day. The conversation in this workshop provided several ideas for how to manage classroom activities for students who miss class or choose not to participate in activities. Interactive notebooks replicate a scrapbook for algebra learning, although the tools could be applied to any subject area. We ended by creating about three Foldables to reinforce topics in a classroom. Amy says she uses the following blogs most frequently:

IMG_0122 IMG_0914 IMG_0121 IMG_0913 IMG_0915IMG_0119 IMG_0120

Debra Schneider & Alyssa Engle
(Evergreen Public Schools — 1500 SE Blairmont Ave Vancouver WA 98683)

A Free Common Core Aligned Algebra 1 Curriculum

A consortium of school districts in Southwest Washington have design a curriculum aligned to the Common Core content and practice standards. We have rich tasks, fluency practice, formative and summative assessment, and professional development modules.

Debra is a curriculum developer in Vancouver who received a grant to develop a curriculum around the common core for Algebra 1, Algebra 2 and Geometry. These are field tested activities and are FREE for any teacher to use. They obtained an open license to allow teachers to use the information for their classroom without additional credit. They have Algebra 1 published this year, next year they will publish Algebra 2 and later Geometry. This is a cool resource which focuses on BIG IDEAS for students and teachers.

This is a link to the free Algebra 1 curriculum and all related materials, there are a lot of very well developed activities on the site. http://swwmathematics.pbworks.com/

 

Dan Meyer
(Doctoral Candidate, Stanford University — dan@mrmeyer.com>)

Better Than Engagement

We try to engage students with math games, math rap, real world math problems, and promises of jobs later in life, but that engagement is often short-lived. The presenter will introduce Guershon’s Harel concept of “intellectual need” – a place where students need new math learning – and ground it with practical strategies.

Dan is an educational profession who is teaching teachers to remove the “Real World” from the classroom because it doesn’t work. He claims that students will better understand the idea if we turn the dial down in education and ask very fundamental questions on a basic level. This is a unique way of thinking and is highly inquiry based which leads students to valuable discussions. I took some notes on his lecture although he is famous in the math community for his TED talk which emphasizes a very similar message as his lecture at NWMC 2014. (http://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en)

 

Day 2 – Saturday

NWMC Day 2

Again, the attached document if for day two of the conference and note I took during the conference. There are a lot of pictures in the document above. These sessions mostly had more visual elements to them. Again, I will comment on each session for important points and provide resources.

 

Nancy Wisker
(Dinah Zike Academy — nancy@dinah.com)

ScafFolding Interactive Math Journals via Notebook Foldables®

In this fast-paced session discover how to transform basic classroom materials and scafFOLD your math instruction using 3- D graphic organizers known as Notebook Foldables®. See the possibilities unFOLD and depart with a mini composition book filled with immediately usable ideas.

This course taught teachers several visual aid and organization strategies to build concepts for an interactive notebook. Foldable’s can be independent of a notebook page or can be pasted in. Some of the topics were elementary and were silly for high school students, but other tools could be easily adapted for any classroom or topic.

 

Katie Akesson
(Cavelero Mid High School — katie_akesson@lkstevens.wednet.edu)

Implement Standards Based Grading into your grading NOW – Including CCSS!

Have you heard about standards based grading and are now ready to do it? This workshop will provide easy, practical strategies to implement standards based grading into your grade-book starting now – even include CCSS.

Standards based grading is important for showing students where they are struggling and where they are excelling. Providing an area in the grade book is important to show parents which areas to work on. Additionally, this talk provided some ideas for classroom management. Katie teaching in a school district where students need to receive feedback on their homework, however the problem with collecting, grading and redistributing papers is a tedious effort on the part of the teacher. Students complete homework as requested and earn a daily score, homework complete (1 pt) or homework not complete (o pts.). At the end of a 1.5 week period, the class has a quiz on a characteristic homework problem. At this time, Katie collects homework packets from the past week and grades a the homework quiz and homework problems. The students may use homework notes on this quiz.

The primary focus of the talk was standards based grading. Katie shared her approach and grading scale for students for tests, quizzes and projects. Students can earn up to 55% by making an effort. Providing student points for effort encourages work, but does not deteriorate their grade to the point of no return. Students can revive themselves from a bombed test or misunderstanding. Incorrect thinking still results in a non passing score, but they still have a chance at learning the information and encourages continued effort.

Another take away from this talk was the style of grading for tests. Each test contains several standards, a grade is assigned to each standard and that is placed into the grade book. For one test, there may be up to four grades. For example, the grade book may read Chapter 4 Test: Solve Equations, Chapter 4 Test: transformation equations and so on. This allows students and parents to really focus in on problem areas.

 

Tom Reardon
(Fitch HIgh School / Youngstown State University — tom@tomeardon.com www.TomReardon.com)

The Great Applied Problem and Several Other Outstanding Individualized Assessment Activities

Creatively implement these exceptional activities into your classroom – Geometry through Calculus. Discover how to create individualized problems – unique to each student – and how to create individualized answer keys including all intermediate answers to easily assess these individualized problems.

This lecture was provided to help teachers provide challenging problems, primarily focused on the higher level math classes such as precalculus and calculus to create individualized problems. The secret, a spreadsheet with the answers. While Tom grades based on correctness of each step along the way, each problem should be displayed as an organized piece of work. Tom also talked about classroom strategies when presenting these challenging problems to his classes. He allows students to work together and carefully watches as students work to problem solve. He takes a hands off approach and lets the students figure out the problems.

He provided resources for us to use in our classroom through his dropbox.

https://www.dropbox.com/sh/4ew97i5kp2ic9rb/AACDppQOlB5PKEURtdv51cAca?dl=0

 

Overall the math conference was excellent, I learned about many application tools which aligned with my university learning. I would highly recommend professionals to attend this event to learn about what other teachers are doing in their classrooms. After many sessions I walked away with great excitement about how I could implement this in my classroom, even adjust the procedures of the classroom for my internship to help students needs. I would have liked to see more research being contributed to some of the lectures (such as Dan Meyer’s Lecture) however I think many of the presenters at this conference were genuine in their interest to help students and improve other’s pedagogy for teaching math.

Big takeaways:
  1. Interactive Student Notebooks, similar to what we do in class, but modified to provide more structure. Essentially creating student created textbooks in a journal.
  2. Dan Meyer presented about introducing mathematical concept in an engaging way that doesn’t necessarily have application, but makes students think about an interesting question. This provided some resources for unmotivated students who don’t typically engage in classroom activities alone.
  3. Standards based grading, breaking down assessments and assignments into chunks of what we want students to understand and enter these into the grade book separately. This allows students and parents to clearly see which concepts the student is struggling to understand. So when Student A gets a 75% on a test, he may have gotten 100% on combining like terms questions, but 60% on factoring trinomials.
  4. Graphic organizers for less organized students or students who are more into art. One class structure is to teach organizational tools and study tools to students who need them.

Characteristics of an Effective Educator

According to the US Census Bureau in 2011, more than 79 million people were enrolled in school between nursery and college, that’s 29.6% of the US population. Since a major portion of the populace is engaged in school related activities, it’s essential to look at the characteristics of the 3.3 million educators who teach students every day.

Particularly for secondary school, effective educators are well versed in their content area. They should have deep background knowledge to challenge the most curious student with engaging material but also the ability to break down challenging concepts into elemental chunks. Mandating attendance means all students are present and educators should know how to make their subject relatable. From experience, engaging presentations, activities and lessons foster growth. This is the result of differentiated teaching, changing styles to keep the classroom experience engaging. Most importantly, effective educators show their students they have faults. Being vulnerable in content knowledge can be an opportunity for a teacher to show their students that they are constantly learning as well. Teacher too often don’t ask for help fearing of being ostracized by students.

Teaching is a daily presentation, effective educators come to work with tenacity (the determination to work with challenging students), patience (to serve students in a healthy learning environment) and flexibility (to face challenging situations with grace). These three dispositions are essential for all educators to find success working with students. With an engaging teaching style targeted at all levels of students, the ability to make mistakes in front of students and strong dispositions, these traits combine to be the characteristics of an effective educator.