Charter Schools and a sense of false superiority

    I'm sure everyone at some time has thought to themselves how our public education system failed them or someone they know in some way. As an educator myself I often reflect on how the system failed me (and also how I could have done better myself). The obvious follow-up question is how can it get better? To some, the answer is charter schools. A charter school is a privately run institution that is contracted by the state government and paid for by taxpayer money. While it might seem like a good idea that a privately run institution may provide higher quality education, it seems to me (and this is purely my own speculation) the vast majority of people who think this have very little understanding of how the system works and what research actually says about it. I hope to lay out some of that information in this post.

    Starting with the founding, each state that allows charter schools (currently 45 states and DC) have their own laws which vary slightly but the basic formula is that a portion of the money collected through taxation for the purpose of state education is redirected to these contracted institutions to help offset the cost of their tuition. Simply put, they are public schools by financial means only. Beyond that, there is often very little oversight compared to traditional state public schools (more on that in a bit). In most states, education founds are already stretched thin. To remove more from public education can only further delay any meaningful improvements, which no one denies there is need of. 

   

    On to my second point, accountability. As a public school teacher, I can attest to the stress and pressure of what feels like constant evaluations. From administration observations to the statewide standardized testing data, we get put through some serious scrutiny these days. Charter schools, being privately operated, don't have those same legal obligations. I can see the benefit of this, as I often struggle to design my instruction the way I truly want and in line with modern researched data on best teaching practices because the way we are evaluated is still stuck in the past. While I or my peers may be teaching well or better than traditional methods of teaching, we may lose points on the evaluation because it doesn't match what they are looking for. This sort of pressure doesn't exist to the same degree or even at all within charter schools. Which in theory sounds nice but in practice, research has shown that students at charter schools perform at the same level or worse than public schools across similar metrics.

    Another point people think of when charter schools are mentioned is that they are an alternative for urban school districts and a "way out of poverty" for some students. The problem here is that because these schools are privately run and don't follow the same laws public schools do, they can pick and choose the times of students they enroll and keep. This not only shatters the illusion of some magic ticket out of a failing system but also skews their data by not having to accept students with disabilities and handicaps. The standards taught as such schools can wildly differ from their public counterparts, sometimes even pushing certain biases rather than teaching facts and letting students form their own conclusions. 

    Overall, charter schools were a decent attempt at fixing a broken system but their time has passed. Instead of looking to take even more resources from our already strained public systems, politicians and people should be encouraging more funds and resources as well as a culture shift in the way we are forced to conduct our trade. There is a plethora of data available showing that we can do education better if we are brave enough to accept a different way of teaching but that would mean a drastic change in how we teach, evaluate, and grow our students into life long learners, not just graduation numbers for the state.

Charter Schools Are Not Public Schools

The Battle Over Charter Schools

Do Charter Schools Get Better Academic Results Than Public Schools?

What is Learning and How Do I Promote Optimal Learning?

What is Learning and How Do I Promote Optimal Learning?

Currently, I teach secondary level mathematics at a public high school. In what follows I will describe what I believe and understand what learning is from both research and personal experience. This theory of learning impacts my decision-making as an instructor and is in continual re-evaluation as I continue to learn from putting this theory into practice. It is my experience that learning is a complicated and involved process and while there are many theories that attempt to explain how learning works, none are fully complete by themselves. My best attempt to build a framework for the learning process would be a combination of Constructivism and Cognitive Learning Theory (CLT). I believe these theories best capture the complex thinking process and explain how best to reach higher-order thinking skills in our students.

The Learning Process

To understand my view on the learning process, I will start by defining both Constructivism and CLT. Constructivism says that learners will more or less construct their own knowledge based on influences experienced by the learner. This knowledge is mostly subjective and may not be factual depending on the influence the knowledge was constructed from. Constructivism is broken down into two main areas of knowledge construction known as individual constructivism and social constructivism. Individual constructivism, also known as cognitive constructivism, centers around knowledge constructed by the learner's interactions with the world around them. This form of constructivism is largely attributed to theories developed by Jean Piaget. Piaget believed that as a learner responds to external stimuli, knowledge is formed through a process called adaptation. This adaptation is the organizational process of acquiring new knowledge into knowledge structures called schemas. These new schemas are either assimilated, added to our existing knowledge, or accommodated, meaning our existing knowledge changes according to the new schemas being formed.

The second form of constructivism is social constructivism which explains that knowledge is constructed through social interactions such as classrooms, families, friend circles, etc. Knowledge constructed this way was best explained by a Soviet psychologist Lev Vygotsky who strongly argued that the social environment is an integral part of the learning process. He defined a higher-order learning process called signs and tools. Signs are the internally-oriented constructs that help learners gain knowledge from their social environment while tools are externally-oriented constructs. Another key idea Vygotsky provided was defining the zone of proximal development (ZPD) which states that there are different stages of learning. The first stage is the knowledge you can gain by yourself without any help. Second is the knowledge that you can only gain with the help of more knowledgeable others. Last is a zone of learning that is simply out of the learners grasp no matter how much support they receive, at least for the time being. This ZPD is what leads to, in part, the idea of scaffolding in education today. Possibly his most important impact on the understanding of the learning process is internalization. This process is best described as “the internal reconstruction of an external operation,” meaning a learner transforms external knowledge or stimuli into some internal understanding of the world around them (Vygotsky, 1978).

This leads me to the second learning theory I will primarily focus on, cognitive learning theory. This theory holds that the learning process is a natural byproduct of learner's attempts to comprehend the world around them. As a result, learners are active in the learning process by experiencing and observing. This requires deeper learning processes of interpretation, evaluation, and experimentation. The key notion is that learning does not happen in a vacuum.

  At the core of CLT is a focus on memory and how it is developed and maintained. Richard Atkinson and Richard Shiffrin developed the information processing theory (IPT) through their self-named model. Their model helped explain why some memories seem to go in one ear and out the other, why some can be retained for a short period, and while others are retained long term. Memory is broken up into stages of sensory, short-term, and long-term memory. The process starts with sensory memory, background knowledge gained through some stimuli such as sight, smell, sound, etc. Sensory information only becomes short-term memory through an intentional focus on that sensory stimuli and is retained for only a few seconds. This information is only stored in long-term memory through some form of rehearsal. Once stored in long-term memory, this knowledge must then be recalled back into our working memory, or the memory that currently has our focus and attention. The flow of knowledge through this memory process is of great importance to teachers. Understanding this process will help teachers with preparing their students to store important information into long-term memory as well as recalling it into their working memory.

It is my belief that the combination of these two theories of learning, constructivism, and the CLT show us the learning process of how students first gather new knowledge as well as how they store that knowledge and are able to recall it. Utilizing these theorems in my classroom, I intend to help students acquire new information by providing as many hands-on experiences and problem-based learning opportunities as I can. There is a growing amount of research showing that problem-based learning in mathematics leads to higher levels of student engagement, autonomy in learning, curiosity, and many other outcomes desired by teachers. In research conducted by Carmel Schettino on problem-based learning, Schettino found that “for many of the students, having a mathematics classroom that focused on curiosity and inquiry instead of processes changed the way they viewed mathematics as process driven, allowing them to take advantage of their creativity for the first time” (Schettino, 2016). This coming school year I will be teaching algebra II for the first time and intend to use this style of teaching. Algebra two topics lend themselves heavily to real-world applications in which students can practice problem-based learning. My goal is to provide problems that will require scaffolding of new material in order to find the solutions. Some of these problems will be well-defined, meaning they have one solution, while others will be ill-defined with multiple possible answers, allowing students to truly use what they are learning in a more authentic way. The scaffolding of these problems will require students to constantly recall prior information, aiding in their storing of knowledge in long-term memory.

In order to track the progress of my students learning through problem-based learning, I plan to utilize mathematics portfolios. While common in both the arts and humanities, implementing and keeping a mathematics portfolio is a young but growing practice in secondary mathematics and is far more common at university level programs. Still, the benefits to student learning can prove useful even at the high school mathematics level. Traditional student assessment in a mathematics course is largely or even solely qualitative. Give the student homework to complete, a quiz for formative assessment, and a test for summative, as these assessments create easily usable qualitative numerical data. A mathematics portfolio however opens up data for teachers beyond the qualitative. A student portfolio could and should include written reflections to help gather data on student thinking. These reflections could be a student correcting missed problems on a previous homework assignment where they not only show work to correct the problem but also write a brief explanation of what went wrong the first time and how they were able to correct their error. Students could also write short, one-page essays on the progress of the problem-based learning assignment, detailing what they have learned about the problem itself in context to the real-world application and what mathematics has been applied to help solve it. The number of ways to collect both qualitative and quantitative data through the use of a mathematics portfolio is diverse enough to allow teachers to get a more comprehensive insight into the various stages of the learning process in their students. My goal of using a mathematics portfolio is two-fold. As an instructor, it allows me a deeper insight into my students’ thinking and understanding of mathematics. For my students it serves the purpose of giving them opportunities to reflect on their own learning process and progression, explaining what they have learned and done in a more comprehensive and connected fashion than traditional assessment can.

Higher Order Thinking Skills

The approach to teaching and the learning process as outlined above touch on the concept of higher-order thinking and how I will encourage my students' growth in this area. Higher-order thinking is an order above simply learning and reciting information but pushes the learner to think critically and creatively, to reflect upon their own learning and understanding, and to utilize skills of metacognition. The latter is a somewhat modern idea in thinking and experiences which “refer to a person’s awareness and feelings elicited in a problem-solving situation (e.g., feelings of knowing), and metacognitive skills are believed to play a role in many types of cognitive activities such as oral communication of information, reading comprehension, attention, and memory” (Schneider, 2010).

One of the reasons I plan to incorporate a problem-based learning approach to my teaching this coming year is to help students develop these higher-order and metacognitive skills. When students have to continually use prior mathematical knowledge in order to discover and understand new mathematical knowledge to find a solution to that problem, they are relying on critical thinking skills to incorporate that new knowledge into their existing schemas. This is further compounded in their portfolios when they will be asked to correct a previously incorrect solution and provide a short explanation of why they got the problem incorrect originally along with how they came to the correct conclusion. They may think they are just putting their thoughts or processes into words but what they are actually doing is performing metacognitive skills of reflecting on their own thinking, adapting their thinking to new knowledge, and correcting prior misconceptions based on that reflection. My hope is that over time, students will begin to more naturally reflect on their own reasoning and catch misconceptions earlier and on their own, building mathematical confidence in not just finding a solution but discovering a process which is really what mathematics is all about.

As students present these reflections to me through their portfolios at regular intervals, I can begin to see their progress in developing higher-order thinking skills. The data gained, both qualitative and quantitative, will assist me in my own growth plan as well as assisting the students in theirs. It is very tempting as a fellow mathematician to simply provide an answer to a solution. But as a teacher, it is my job to guide my students to discover the answer for themselves. If they are struggling with self-reflection, I can provide them with guiding questions for developing metacognitive skills. Vanderbilt University’s Center for Teaching provides a decent starting guide for getting students to think about their own thinking. First, encourage students to describe what they already know about a given topic. Next, ask them to identify what the most confusing part of the material is to them. After a lesson, you can ask then to reflect on how their understanding of a topic has changed or grown (McDaniel, 2020).

 

Complex Cognitive Processes

Another goal of prioritizing problem-based learning is to have more opportunities for collaborative learning among my students. All too often group work can feel forced. When there is an ill-defined problem at hand, collaborative group work is key for developing a comprehensive solution. Students, if given the creative space, will often naturally utilize divergent thinking, where each student will bring to the group their own perspectives and knowledge. During these types of assignments, groups will be encouraged to explore various solution paths at first, using divergent thinking to approach the problem. Using metacognitive focused questions, groups will be challenged to think critically about each solution path to begin narrowing down to one. A short reflection will be assigned for each of these ill-defined problems asking students to express their process of coming up with ideas and how they went about deciding which one to ultimately use.

As students progress through problem-based learning, they will be discovering new mathematical processes and relationships which will later be discussed and formalized on their own. Part of mathematics will always be learning and memorizing key theorems and operations along with their relationships to each other. To aid in this development, students will prime their memories with daily warm-ups. This could be something along the lines of a math-related logic puzzle, a short mastery check on their content knowledge tied to a standard, reflection time on a previous day's lesson, or some other activity which causes students to recall knowledge gained from earlier in the class.

Conclusions

While I believe there is no singular explanation for how an individual learns and processes information, constructivism and cognitive learning theorem combine in a way that helps explain how learners first gather new information through individual or social constriction and then process that information to be stored and recalled into memory. Using these theorems in tandem, I design my class to be focused on individual and collaborative exploitative problem-based learning. Students will spend time reflecting on their learning and thinking through the use of a mathematics portfolio where they will have to explain their reasoning through short writings. Data gathered from these portfolios will guide my instruction by helping me understand what the student understands. I will be better able to assist my students by asking metacognitive based questions to further their own understanding of their unique thought process.

References

Burks, R. (2010). The Student Mathematics Portfolio: Value Added to Student Preparation? PRIMUS, 20

Carey, S., Zaitchik, D., & Bascandziev, I. (2015). Theories of development: In dialog with Jean Piaget. Developmental Review, 38(C), 36–54. https://doi.org/10.1016/j.dr.2015.07.003

Chick, N. (2020, March 27). Metacognition. Retrieved from https://cft.vanderbilt.edu/guides-sub-pages/metacognition/

Dunn (take from Canvas)

Izawa, C. (1999). On human memory evolution, progress, and reflections on the 30th anniversary of the Atkinson-Shiffrin model . Lawrence Erlbaum Associates.

McGilly, K. (1994). Classroom Lessons : Integrating Cognitive Theory and Classroom Practice. MIT Press.

Richardson, V. (2001). Teaching: Trends in Research. Retrieved from https://www-sciencedirect-com.proxy.lib.utk.edu/science/article/pii/B0080430767024530

Schettino, C. (2016). A Framework for Problem-Based Learning: Teaching Mathematics with a Relational Problem-Based Pedagogy. Interdisciplinary Journal of Problem-Based Learning, 10(2), 27. https://doi.org/10.7771/1541-5015.1602

Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM, 42(2), 149–161. https://doi.org/10.1007/s11858-010-0240-2

Schunk, D. H. (2000). Learning theories: An educational perspective (3rd Ed.). Upper Saddle River, NJ: Prentice-Hall

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

Virtual Classroom Management

I was going to write this blog about traditional classroom management as that is something I’ve spent a lot of time thinking about this year. Instead, I will shift the focus slightly to something more relevant given today’s teaching environment, digital classroom management. A report from the National Center for Education Statistics says that in 2017 “about 21 percent of public schools and 13 percent of private schools offered any courses entirely online.” This number has only increased since then and more so due to COVID complications. Being able to skillfully use what we know about classroom management in the online learning environment will be a significant tool for teaching this coming school year.

According to the team at Edutopia, the proven practices of in-person classroom management should not be discarded simply because of instruction transitioning online. In our physical classroom, we often design and us the space available to us intentionally to build an atmosphere of learning. The same can happen online by providing clear areas for your online students to find the resources they need. This may mean preparing a very thorough tutorial video showing students where all of their resources are since they might not be clearly visible like in a physical class.

Photo from Study.com

You still should encourage a community mentality within your students. Groups can still be assigned as we would in person and the same mentality of intentional grouping should be put into practice. Most online classroom software has options for setting up groups. It might be okay for randomly assigning groups for smaller short tasks but for more engaging purposing use the data you have about your students just like you would in person. 

    Just like you would do with a physical classroom, you need to have clearly defined online office hours and contact information so your students know how and when they can reach out to you. Be present when you are working with them virtually, minimizing as many distractions as possible in both your environment and theirs. Since you won’t be able to chat up your students in the halls, be sure to reach out to them regularly through a variety of means. 

The general rule of thumb, if it works in a physical classroom it works in an online one. As a teacher, you might have to learn some new ways of establishing your classroom management plan when doing distance learning and adjust your own habits accordingly but in the end, your students will adapt under your guidance and examples.

Course management for the Online Classroom

Extending Classroom Management Online

National Center for Education Statistics

Distance Learning - Does it have a place in k-12 Education?

Due to COVID-19, there is certainly more discussion on the use of distance learning in our k-12 education system than ever before. Generally speaking, I see two camps of thought here. The first is embracing this forced change as a way to embrace the future of grade school education. The other is that it can not replace in-person education and we should return to business as usual ASAP. In this blog post, I will discuss the pros and cons of each of these views as well as my own opinions on them.

First, let me address the real short-comings of distance learning in K-12. As everyone was quickly forced into distance learning this spring due to COVID and schools began looking for answers, there really was only one choice. Moving learning to online on short notice high lights many of its faults. If a district is not 1-to-1 (meaning every student is given a laptop or tablet for schooling) then that leaves out any student who does not have access to a computer at home. Even still, many students, especially high-risk ones, don't have the internet at home making them unable to attend to their school work. These issues are logistical in nature and could be dealt with by proper school founding but we all know that uphill battle. 

The real issue at hand with utilizing distance learning in K-12 is the lack of proper training. The typical teacher is trained in educational theory grounded in facility-based education, not in online teaching. While some principles absolutely transfer to any realm of teaching, research points to best practices for online teaching that you simply don't think about when doing in-person learning.

Now on to the bright side of things. There are many positives to our current situation which causes us to reimagine what education looks like during times were in-person. Distance learning has already been used in certain areas of K-12 for years such as homeschooling, really small populations where teachers are often shared between schools, youth who are unable to attend traditional school for whatever reason, and many more. Some schools have gone entirely online saving money on facility costs that they spend on resources and keeping teacher to student ratio low. There are even emerging studies showing that, if done right using research-based best practices, distance learning can be as effective if not more than traditional facility-based instruction.

In my opinion, there is a happy middle-ground of facility-based instruction and distance learning instruction. There are certain things you just can't do online such as working on group projects that require in-person collaboration. Having a dedicated physical location where students could work collaboratively during problem-based learning with the teacher facilitating just makes sense. But a large portion of learning and instruction could be carried out online thanks to all of the modern tools at our disposal, both paid and free. As classroom sizes continue to grow making the teacher to student ratio continue moving the wrong direction, moving some learning to online might help alleviate this modern teaching challenge. Only time will tell what our "new normal" in education maybe, but using this time to better learn and understand how to use modern teaching tools to solve modern teaching problems might be worth the struggle.

References:

A Teacher's Guide to Distance Learning

How Effective Is Online Learning? What the Research Does and Doesn't Tell Us

Exploring the Concerns of Online K-12 Teachers