From the Mind’s Eye of the User is certainly a complex introduction to the theory of sense-making. In it Dervin describes a theoretical framework as concepts and principles justified by prior research and evidence. She then grounds and frames these principles by providing several processes to make the concepts a reality. Her framework directly defies certain conventions and challenges a new perspective on qualitative data, while also critiquing the “standard” form of information systems. These processes give practical steps to realizing her framework and she exemplifies this by pulling from already complete studies on sense-making.
Ultimately, I feel as if Dervins is attempting to communicate a “new” philosophy of research and its principles. I put “new” in quotation marks because I feel Dervin would argue sense-making has always been there, just ignored or misused. Not to mention the forty articles she brings up in her conclusion. It is new in the sense that it challenges a conventional framework, the “versus” framework. It also defies a conventional system structure. We typically, in society, depend on experts. It’s what we do. We get jobs and we become experts at them. Most people have a conceptual idea of what it means to be a teacher, but only teachers actually KNOW what that experience is like. Some days, I feel like I fill out paperwork and write e-mails more than I instruct children. My step-father was a fire fighter at one point in his professional career. Many people have conceptions of what firefighters do, but only those who have experienced being a firefighter or close to a firefighter know that they spent the minority of their time actually putting out flames. They have other important duties as well. The point being, we build a society of experts and rely on them. A non-firefighter does not fully understand the full duties and therefore relies on the firefighter to accomplish them. Since we rely on experts, our systems are geared towards the people who, in theory, need them the most, the experts. Librarians used to rely on card catalogs, which may not be the best for the average person but were certainly effective and useful for librarians who were familiar with the tool. So, naturally, when sensemaking challenges to take things from the viewpoint of the actor and not the observer, it exposes “flaws” in the design of our information systems. Exemplars 2 and 6 indicated this well. In both, a patient repeatedly stated they did not understand a procedure and received no real explanation. Their gap was not bridged, they did not acquire the help or knowledge, and remained with their feelings of suspense of confusion. This is because the system of medical information was not designed for their use, but for the nurses and doctors use. The new mother was given cold water and instructed to walk because her doctors had information stating they were the best methods for her recovery. The new mother, according to this system, did not need to know that for the treatment to be effective. She just needed to comply. It is a results-focused or outcome focused method rather than a holistic and individually-focused approach. Sensemaking begins to critique this. As for my sense-making of the article, I had to read it through, watch the video on the topic, read it again, focus on the exemplars while referring back to the methods description, and read the conclusion twice more. It was hardly efficient, but reminded me of the chunking and analyzing that my philosophy classes in college required, leading me to my conclusion that sense-making is a research PHILOSOPHY more than a methodology. As I type this, I reflect on how I could have done it differently. I also reflect on how (with a little irony) this structure of academic article did very little to bridge my gap on sense-making. It took me as a motivated individual plowing through the provided tools repeatedly to process things. I wish someone had done a timeline interview with me as I was reading it the very first time, it would have been enlightening. In a strange way, I feel like the exemplars did the best job bridging the gap for me. At first, I was stuck on the idea of quantifying the qualitative, but the exemplars helped me see that it was really a perspective shift that allows qualitative things to become qualitative. Starting with some of those, even without the framework presented first may have given me more of a lightbulb moment. If I had to break down this article to a high schooler, I would question the person who was commanding me to do so. Like I said, in a rather ironic fashion, the article’s structure is anti-sense-making to me. I don’t feel like jigsawing the article would be supremely helpful because all the methodologies and procedures serve a larger purpose, highlighting the idea of analyzing qualitative responses through the system the individual was acting in. My students could completely understand the idea of an image survey and miss the dots that form the bigger picture of sense-making. How I would approach this topic, if it was required of me, would be a fishbowl simulation. I would convert some of the exemplars into scripts, have students simulate the exemplars in a small group with the peers watching, and have a discussion about it. I feel like seeing the respondents struggle to get access to information might get students onto the idea of analyzing how information is shared via systems. Then they can move onto analyzing images of companies or tools being presented to actors and start making sense of what the individual is experiencing. I believe students would need to practice seeing things from the actor’s viewpoint via simulation and then work towards making sense of the tools and systems. Even then, this is very heady material and I wonder how different it would be for students with no experience or knowledge of how research is done. Ultimately, I think the magic word her is "differentiation." It is what sense-making is all about at its core, recognizing the individual and adapting to individual needs and experience. Learning sense-making should probably occur in a similar fashion.
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The school I teach at is technology rich and is looking to become more so in the future. We are a BYOD school but are hopefully going to be move closer to a 1:1 model with a check out system for students who are in need of devices. We have an online Learning Management System called Echo that teachers are expected to use on a daily basis. Google Classroom is being activated for our district. All teachers are given laptops and projectors and my site has been supportive of teachers who request additional technology such as document cameras. We have intervention classes with software components and a fully stocked computer lab. Students are given e-mail addresses via Gmail that will be theirs through the end of high school. My site is a PBL site and is becoming a PrBL site in math and my district includes 21st Century Skills in their mission. Students use technology every day. Students use shared space on the internet, such as Google Drive and other apps, every day. The need for digital citizenship training is overwhelming.
The school I teach at is a middle school and every year I have been at this school, without fail, we have had some technology related or social media related student issue. Whether it is cyber bullying via Twitter or Instagram or students bashing on teachers in Google Docs or Chat or even things as serious as sexting, students can take their tech use too far without boundaries and training. One year, a student who was in excellent academic shape and had won awards got involved in one of these technology mishaps. It will surely follow him for a long time. I have no doubt that without digital citizenship, more students will wind up like him. Fortunately, my site values digital citizenship. In sixth grade, students complete a digital citizenship project in social studies, focusing on how to use technology professionally and manage their footprints. In seventh grade Language Arts, students do an argumentative project about social media. Yet despite this, students still get into trouble each year. I do not believe there are any shortcomings to the wonderful projects at my site, but maybe students need more. Or maybe it is just a middle schooler’s nature to push boundaries until something snaps back. Either way, the course of action is clear. Students need consistent digital citizenship training in all classes and all content areas. When I reflect about digital citizenship and math, it feels difficult at first. Common Sense Media links all their activities to ELA standards, but not to math. There could be some interesting work in statistics of identity theft, but making students aware of identity theft is not necessarily digital citizenship. Teaching students how to protect themselves against identity theft is closer to digital citizenship and that is something math can help with. Every year, before even thinking about digital citizenship in my own room, I had students do a Problem Based Learning Unit on password strength and why longer and more complex passwords are so valuable. Ironically, students learned that their assigned passwords were not incredibly strong and made many of them glad they changed them. This connected well to mathematical standards on sample space and probability models and begins to get on the fringes of digital citizenship. While being safe and secure online is a foundation of digital citizenship, I believe more can be done. A second idea for integrating digital citizenship could be using Google forms to create surveys. I would prefer this to Padlet because it can export to Google Sheets while still allowing the anonymity of Padlet. Then the data can be organized and used in a structured way. Teaching students to use Sheets also increases their digital agency and 21st Century skills. Ideally, students could design their our survey questions. Perhaps questions like “How many social media accounts do you have?” to show how wide a footprint can be or “Have you ever had a negative experience on social media?” to show the prevalence of cyberbullying in their community. This could help make the issues more authentic for students by seeing data that relates to their classmates. Then they can create charts to demonstrate evidence and make mathematically supported arguments about cyberbullying or other topics that they are interested in. A third idea I have is less mathematically inclined, but still can develop useful skills. This resource from Common Sense Media, which I want to build into a lesson plan soon, does not include math, but is very similar to what my site calls a “Claim-Evidence-Reasoning” process. We do it in all subject areas to help prepare students for the CAASPP and beyond. Students need to put together a claim and research evidence to support it. The evidence they choose is justified by their reasoning. This activity has students do just that. Students need to make a claim about which host to do, find evidence for their claim, and provide reasoning to support their evidence. This activity is perhaps more intuitive to students than some math problems and can be a great way to scaffold and practice the CER process with them. This option is the least personal of the three, but i could add reflective journals to it so students can relate the problem to their own experiences. I don’t feel like any of these ideas particularly tie into digital communication directly. The third idea gets into the idea of “passive” communication where public information has an impact on your opportunities. The second idea could tie into the effects of previous communication on social media. If I needed to focus more heavily on communication and wanted to do it in a mathematical way, perhaps I could focus on infographics and how students can effectively communicate via digital products. Most students do not understand what makes an infographic effective and clear at first. While that is more niche than say, professional e-mails or social media postings, I believe that it is a part of digital literacy and impacts a student’s digital citizenship. In other words, citizenship can show up in a lot of ways. The more literate students are with different apps and forms of information sharing, the more they can participate. A student who knows how to code has different opportunities online than a student who designs graphics than a student who runs a blog. However, all those different skills can impact a student’s citizenship and I imagine that digital citizenship will only continue to expand as time moves on. As a math teacher, competency based learning feels like a Holy Grail. I want my classroom to be self-paced, I want my students to not waste time sitting through notes when they already understand the material perfectly. Math is fairly unique in that it is super progressive. If a student has master 7th grade content, why shouldn’t they move onto 8th right away? Most people seem to answer “well, then they will be bored next year…” That feels like a weak answer to me.
I feel like math is on the road to competency based learning. Softwares like Khan Academy and Prodigy both allow for individualized assignments, self-paced learning, and individualized rewards systems. Other game based learning systems like Lure of the Labrynth also allow students to work in a learner centered away. Even better, all these things are totally free for the classroom! There are some struggles still of course. Can a video module every truly replace teacher interaction? How do you build a culture where every student is confident enough to ask for help when needed? Some systems have great feedback tools, but they can only provide feedback when a student provides input. What about the equity of technology at home? I feel like making a learner-centered environment without technology would be resource intensive (lots of printing). I wonder if, in the constraints of the public school system, it is possible to have a truly learner-centric environment. Without the guarantee of equity and access for all students, I have doubts that a tech-rich system is possible. However, every year I am moving closer to a blended approach. I feel like every school year a new learning system pops up. I have gone through Tenmarks (Amazon), Khan Academy, Prodigy, LearnZillion, Lure of the Labrynth, and more in the last 3 years and I’m sure it only gets better with time. When I reflect on the C-Content speakers, I feel like there are several underlying threads. All of them insist we must have cultural change to enable creativity. Specifically, I think they all come back around to the way we treat failure. Some of them refer to it as playing or experimenting and some refer to it straight up as failing, but they all agree it is a necessary thing. It is okay to not have instant success. It is okay to try things, even when they don’t work out. Trying things out is part of learning. Getting experience makes you better. Failing helps you become flexible and reflective. When these elements are absent from a classroom, creativity is stifled or worse, completely absent. A second theme I notice running through all the speakers is the idea of motivation. They all speak to students having choice, driving curriculum, making things that are meaningful. Nothing stifles creativity like meaningless work. Students need to feel motivated in order to be creative. They have to believe what they are doing matters. The carrot and stick dichotomy no longer work. Educators cannot encourage creativity by threatening students with disciplinary or grade related consequences.
When considering Mobley’s 6 insights, I feel like what Hammond says about the purpose of our education system is relevant. Our education system was designed to churn out laborers and workers. Not inventors or scientists or problem solvers. Mobely’s first point is that traditional teaching goes directly against building creativity. His second point is that creativity becomes an “unlearning process.” In our education system, with number of standards and the need to pass curriculum assessments, we never take the time to unlearn and think. Unlearn and approaching content from new perspectives takes time and we simply do not allow for that time. We are learning forward as fast as we can. The rest of his points about becoming creative, surrounding yourself with creative people, and being reflective are all fully possible in the school system. Nothing says that we cannot reflect or collaborate within the classroom. However, unless the first two points are present, there are no creative people to surround yourself with. Without creative people around, becoming creative is that much more challenging. We can still reflect and many school have some type of reflection, in the form of a portfolio or at least Open House. However, that reflection does not build creativity unless there are creative projects and collaboration to reflect on in the first place. Essentially, I can see creativity becoming a thing in public education. I even see it in some schools and individual classrooms, in some content areas more than other content areas. However, in order to make creativity something that can extend to all students in all contents, which we need to develop mathematical and scientific problem solvers, we need to reimagine the structure of public education. Without room to be wrong or to unlearn or to reflect on new perspectives, students will not have the opportunity to develop those creative muscles. Darling Hammond concludes her commentary in the Flat world and Education with 5 key elements crucial to the success of a hypothetical (and hopefully eventual) reform of education in the United States. Below, I will dive briefly into each of them, but first I want to take a moment to reflect on the process of reading The Flat World as a whole.
Firstly, it has been a thoroughly validating process. I definitely consider myself to be a social justice minded individual. Personality tests or self assessment books on rivers of motivation always point me in that direction. When in the classroom, many people want to complain about how difficult teaching is or talk about what heroes teachers are. While I agree that in general teachers are overworked and can have a large impact on children, I have always felt that there was more to be done. That despite bringing work home or lying awake at night thinking about lesson plans or giving up lunches to work as a mentor at our wellness center that it just wasn’t enough. That there were bigger issues. It is validating to hear those issues laid out. It is also a little frightening. That book is already seven years old and was building off decades long trends. And the data has not changed much in the last 7 years. I see change all around and I believe it is a step in the right direction but sometimes I wonder if it is enough. How much more can we squeeze out of the current education system without deeper and wider reform? These are questions I suppose only time can answer for now. The first element Hammond discusses is Meaningful Learning Goals. Something that really sticks out about this is another striking comparison to other education systems in th world. Successful educational systems tend to focus on fewer learning goals per year, but make each one deeper and more meaningful. They focus on a broader spectrum of habits of mind and leveraging those to push deeper into content. In America, we have cut back the number of standards since the No Child Left Behind days, but have not made sweeping pedagogical changes towards reasoning and inquiry. Some sites are doing it well, some organizations are championing the 4 C’s and student driven classrooms, but on the whole it is a bay step in the right direction My site is currently pushing into Inquiry learning in Math, but even with the standard number reduction from Common Core pacing is crowded. We seem to be in a catch-22. State testing measures problem solving and reasoning, but students can’t demonstrate those if they have not learned what a scale drawing is or how to build a probability model. There is a fine line between covering all the material and focusing too much on inquiry. Students cannot be expected to “discover” certain aspects of math. Another element Hammond brought up is accountability. This one leaves a bit of a bad taste in my mouth. No Child Left Behind was an example of accountability gone horribly wrong. It lacked the supportive element Hammond describes in other systems, such as Finland, Singapore, and Korea. Accountability cannot just be punitive, it needs to go both ways. Schools need to be accountable for growth in performance but the system needs to be accountable for providing the resources and environment to support that growth. If schools are underperforming, train educators to be better and reform curriculum. Examine financial policies or clean house if need be. Don’t strip funding away from the students who need it most. That is “hands-off” accountability and there is a reason why it is not present in high achieving systems. I believe the element of accountability goes hand in hand with strong professional support. In fact, they are two sides of the same coin. The best systems in the world invest in the professionals who run that system. Teachers endure massive pdagogical swings every decade. From inquiry based to rigor based and back again. Most teachers who don’t like Common Core make comments like “We’ve tried this before and it was no good” or “It’ll be around for a few years and we will move away from it again.” That is indicative of a larger problem. We abandon curriculum and pedagogy without training teachers to succeed with it. They are hanging onto the swinging pendulum of curriculum. It is common for districts to update curriculum every 7 years, not a bad thing, but certainly something that requires a continuous cycle of training to keep professionals on their toes. The logistics of improving professional support is complicated and not an issue I’m qualified to tackle, but it is abundantly clear it is one of the most essential for truly changing the core of American education. International Context
Internationally, the American education system has seriously underperformed other comparable countries. According to TIMSS, America ranks at #11 for 4th grade student performance and #8 for 8th grade student performance of all countries that participated in TIMSS and TIMSS Advanced. While scores have shown long term improvement over the last twenty years, scores plateaued heavily during No Child Left Behind and have not measurably improved from 2011. As Darling-Hammond also illustrates, countries that currently outperform America have varying styles of education. This suggest there are many factors such as culture and economy that go well beyond the walls of the classroom. Thus, non-academic factors, such as a growth mindset, merit exploration. Another point of interest from the TIMSS study is that the bottom 25% of students are the ones who are experiencing the most drop off in their scores. The upper 25% has continued to grow steadily to preserve the overall average, but the inequity in mathematics education is apparent. National Context National data supports the findings of TIMSS. In fact, NAEP shows scores actually dropped between 2013 and 2015. The scores are higher than in 1990, but have not been measurably improving yet with the implementation of Common Core. NAEP data is also consistent with the data from TIMSS showing that the bottom 25% of students are falling off rather than improving and that minorities continue to struggle in the American education system. Boaler and Sengupta-Irving (2016) found that low achieving students in math and science tend to wind up in low pay and skills oriented jobs. The development of Common Core began in 2009 as an equity issue. States all had varying standards and varying definitions of proficiency. This was one of the driving forces behind the development of the Common Core State Standards which would begin to be ratified and adopted starting in 2011. The Common Core standards put a strong emphasis on deep, conceptual learning and less emphasis on formulaic thinking and skills. This complements the problem solving structure of PrBL. The grit developed from a growth mindset also enables students to go deeper with concepts and curriculum. In 2001, the Partnership for 21st Century Skills (P21) was formed. P21 is an organization focused on promoting the 4 C’s, Life and Career Skills, and Technology Skills for students. This framework for students also synergizes well with PrBL and a growth mindset. PrBL frequently uses technology to enable more authentic problems, relies on students to use agency and collaboration to tackle larger tasks, and introduces or prepares students for future opportunities in college and career. State Context In California specifically, the data is less optimistic. In mathematics, for grades 6-8 in 2016, less than 40% of students meet or exceed academic standards. More than 25% in each grade level fall into the Standard Not Met band. When examining the CAASPP’s three mathematical claims, the outlook is worse. In Concepts and Procedures, more than 75% of students between grades 6-8 are Near or Below Standard. In Problem Solving and Modeling & Data Analysis, 80% of students between grades 6-8 are Near or Below Standard. Finally, Communicating Reasoning also has 80% or more students between grades 6-8 at Near or Below Standard. While the data is not acceptable in any category, Problem Solving and Communicating Reasoning are the worst for students between grades 6-8. Drilling down into at-risk minorities makes the data spread even less favourable. Problem-Based Learning A study in Problem-Based Learning (PrBL) in Mathematics may provide information toward improving student performance. In the study, 271 students were given several PrBL units, to see if this instructional mode would reveal any previously unidentified academic potential. Findings from the study suggest that well-designed PrBL can reveal unseen potential in students. (Gallagher, 2013). This potentially can address the disparity of the bottom 25% as noted in TIMSS and NAEP. PrBL also breaks away from more traditional forms of instructions and instead focuses on open ended problem solving. This lines up with the CAASPP’s increased focus on claims and reasoning. Boaler and Sengupta-Irving (2016) also found that increasing student agency and collaboration in heterogeneous groups improved engagement and achievement in mathematics with middle school students. The researchers also noted that students responded with more enjoyment to mathematics when they were given responsibility and collaborative opportunities. Mindset Self-concept is another factor that studies have shown to impact student achievement. Pinxten, Marsh, De Frain,Van Den Noortgate, Van Damme (2013) found that positive self-beliefs about math competencies had a positive effect on math achievement and a negative effect on perceived effort expenditure. Math enjoyment was also found to have a smaller positive effect on math achievement.The study focused on over 4,000 students between third and seventh grade. This further emphasizes the need not only for a pedagogical shift, but a mindset shift in education. Parker, Marsh, Ciarroch, Marshall, & Abduljabbar (2013) found in a longitudinal study of Australian youth that self-efficacy in math served as in indicator for future achievement. Specifically, math self-efficacy could be a strong predictor for university and post-graduate studies entry in STEM fields. This directly speaks to the long term importance of improving math self-efficacy. Growth mindset can be referred to as a specific type of self-concept. Dweck, in a 2014 continuation of her original work on growth mindset, found that high school students with a growth mindset were more likely to recover from receiving poor grades. Dweck also found that growth mindset predicted higher academic achievement via grades and SAT scores. This improvement was attributed to growth mindset students’ use of deeper learning strategies. Not only that, but girls and minorities seem to benefit more from a growth mindset, which helps level the playing field that has been skewed against them for decades. (Dweck, 2008). Claro et al. (2016) found that growth mindset also can reduce the negative academic impact of poverty on students in education. In the study, researchers also ran a reverse causation and found that growth mindset is not just apparent in successful students. In short, growth mindset causing success is not due to confirmation bias of successful students. Research by Yeager et al. (2012) has also shown that this growth mindset can lead to greater resiliency when facing mathematical challenges and, thus, can lead to higher rates of course completion. Beyond just improving performance on international testing metrics, growth mindset can create long term impacts by getting students farther in education. Local Context and Response The study district has slightly more favorable data than the state averages, with just over 30% of students in the Standard Met or Standard Exceeding Band in the Mathematics domain. study school has slightly more favorable data than the rest of study district, but not enough to be significant. However, study district still has more than 50% in the Nearly Met or Not Met band, so there is still a problem to address. Students need to continue to improve in their their ability to Problem Solve and Communicate Reasoning. study district has partnered with the New Tech Network to further implement 21st Century Skills in support of the Common Core. The study school is a Project Based Learning and Problem Based Learning School. Teachers have been to trainings and conferences provided by the New Tech Network and worked with consultants to develop authentic and rigorous PBL and PrBL units. The study school is currently examining how to engage students in cognitively complex tasks via training on Marzano’s The Highly Engaged Classroom. In sixth grade, all students complete projects to inform them about growth mindsets and to begin to develop them. All intervention classes have growth mindset components to their curriculum. Developing a growth mindset is a lifelong task, so growth mindset development needs to be a focus in the classroom at all stages of a student’s education. Problem Based Learning in Mathematics need to continue to develop. In mathematics, students need to learn how to think and write like mathematicians, improve in Problem Solving and Communicating Reasoning. Developing a growth mindset is a lifelong task, so growth mindset development needs to be a focus in the classroom at all stages of a student’s education. Problem Based Learning in Mathematics need to continue to develop. In mathematics, students need to learn how to think and write like mathematicians, improve in Problem Solving and Communicating Reasoning. Completing this Literature Review and Introduction had a dramatic impact on the direction of my paper. Initially, I had wanted to focus on standardized testing because it was a reliable and unbiased measure, at least in respect to me as a researcher. However, this lit review showed me that was a pretty well drawn out area of research and my particular population did not add much of significance. However, this prompted me to look beyond standardized testing into Claims data. This gave me a new direction. Students nationwide struggle in demonstrating their reasoning and problem solving. This lines up well with the PrBL at my school site and my personal desire to instill a growth mindset in students. Growth mindsets can build confidence and efficacy, which research shows are good predictors for future academic success. This also gave me direction on how to properly introduce a growth mindset. It has become a buzzword in education. So much so that Dweck has written several editorials about the dangers of the growth mindset movement she pioneered. Being well informed and prepared to implement my research question properly gives my study a stronger chance to make an impact on my students! My driving question focuses on the relationship between growth mindsets and performance levels on performance tasks. Below are the international, national, state and local contexts for math performance.
Internationally, the American education system has seriously underperformed other comparable countries. According to TIMSS, America ranks at #11 for 4th grade student performance and #8 for 8th grade student performance of all countries that participated in TIMSS and TIMSS Advanced. While scores have shown long term improvement over the last twenty years, scores plateaued heavily during No Child Left Behind and have not measurably improved from 2011. As Darling-Hammond also illustrates, countries that currently outperform America have varying styles of education. This suggest there are many factors such as culture and economy that go well beyond the walls of the classroom. Thus, non-academic factors, such as a growth mindset, merit exploration. Another point of interest from the TIMSS study is that the bottom 25% of students are the ones who are experiencing the most drop off in their scores. The upper 25% has continued to grow steadily to preserve the overall average, but the inequity in mathematics education is apparent. National data paints a similar picture. NAEP shows scores actually dropped between 2013 and 2015. The scores are better than 1990, but have not been measurably improving yet with the implementation of Common Core. NAEP data is also consistent with the data from TIMSS showing that the bottom 25% of students are falling off rather than improving and that minorities continue to struggle in the American education system. Math education is becoming even more of an equity issue. In California specifically, the data gets worse. In mathematics, for grades 6-8 in 2016, less than 40% of students meet or exceed academic standards. More than 25% in fall into the Standard Not Met band In the Concepts and Procedures claim, more than 75% of students between grades 6-8 are Near or Below Standard. In Problem Solving and Modeling & Data Analysis, 80% of students between grades 6-8 are Near or Below Standard. Finally, Communicating Reasoning also has 80% or more students between grades 6-8 at Near or Below Standard. While the data is not acceptable in any category, Problem Solving and Communicating Reasoning are the worst for students between grades 6-8. Again diving deeper into the data show minorities are suffering. The development of Common Core began in 2009 as an equity issue. States all had varying standards and varying definitions of proficiency. This was one of the driving forces behind the development of the Common Core State Standards which would begin to be ratified and adopted starting in 2011. The Common Core standards put a strong emphasis on deep, conceptual learning and less emphasis on formulaic thinking and skills. This complements the problem solving structure of PrBL. The grit developed from a growth mindset also enables students to go deeper with concepts and curriculum. In 2001, the Partnership for 21st Century Skills (P21) was formed. P21 is an organization focused on prom oting the 4 C’s, Life and Career Skills, and Technology Skills for students. This framework for students also synergizes well with PrBL and a growth mindset. PrBL frequently uses technology to enable more authentic problems, relies on students to use agency and collaboration to tackle larger tasks, and introduces or prepares students for future opportunities in college and career. In the context of Common Core and given the low scores in the Problem Solving and Reasoning claims, it is clear that a change is necessary. Growth mindset research has been going on almost a decade and can consistently point to improving achievement. PrBL has been found to foster "unseen potential" in students. These are two possible factors to explore when looking at the equity issue of math achievement. At NCTM 2016 in San Francisco, I had the opportunity to attend a session on Flipped Classrooms. I remember going because a co-teacher was raving about how much they enjoyed flipped classrooms and there are countless blogs describing why a flipped classroom is the way to teach.
On a surface level it makes sense. For an example, I think about how long I spent going over vocabulary and having students get the definitions down in some form. If they are just copying definitions outright, then it only takes maybe five to seven minutes in class, but then what’s the point of doing it in class? I always try to have some time for students to try and connect new vocabulary to other words from the unit or have students write anti-definitions or have students illustrate an example or contribute to a word wall. Now, my vocabulary time is meaningful and worth my effort and attention as the teacher, but also now pushes the fifteen to twenty minute mark! Imagine freeing up those minutes by flipping their vocabulary activities or being able to devote more time to the language because problem example notes could be flipped. The appeal is pretty easy to see. This infographic also highlights some incredible pro’s of the flip model. Students can get immediate help on work because it is all done in class. Students can take their time with their notes because it is a video that can be paused or jumped back. Teachers can spent less time fighting for the attention of a large mass of diverse learners and instead spend their time giving instruction at a level that is relevant to smaller groups. Not to mention, all podcasts and screen recordings can be re-usable in future years! When put in these terms, it feels like a flip model is the obvious solution to math classroom woes. The most obvious hurdle to implementing a flip is that it assumes students can participate in the flip from home. The entire premise is that notes, lectures, and examples are just as effective when recorded and can be done more independently than actual concept mastery work or projects. Therefore, doing notes, lectures, and examples at home is the most efficient way to structure a class to maximize a teacher’s impact. What happens though when a student does not have internet access at home and, due to family obligations, cannot find a way to get themselves to a public library for an hour to take notes? What happens when, due to poor implementation perhaps, student buy-in is low and they simply do not watch the videos? I fully believe that the model is just as effective as they claim it is when done properly. However, I also recognize that schools do not have control over a student’s out-of-school life. So, I do not believe it is feasible in every situation to implement with quality. I know several of my students do not have internet access at home. I know several of them share a single school device with multiple siblings. I know some of them do not get home until after eight o’clock at night due to extracurriculars or parent work schedules. Some of them do not live near a public library and have no adult to take them (and I do not believe that encouraging 11 and 12 year olds to take mass transit alone is a proper solution to making a flip classroom work). I also believe that some concepts are not taught best through video. There some lessons like surface area where I want students hands on with an object to rotate and measure from the very beginning. Not that I believe a flip model would hurt these concepts but I wonder if it really is still efficient if I would intend to re-teach it with manipulatives anyways. I do not mean to speak negatively of a flip model. I have used it situationally before and leveraged it for concepts that I believed were appropriate. Using a flip model for interest formulas was effective for my classroom. However, I struggle with the idea of committing 100% to a flip model. I feel that way about most instructional models. There is no one perfect instructional method for all mathematics and my classroom is a blend of different techniques and practices. If there was one truly superb model, then most of our educational issues would be solved by now. To quickly address Challenge Based Learning, I feel that is more in line with what I am getting at above. Challenge Based Learning is a flexible and blended approach that takes the strength of multiple models. Challenge Based Learning by definition promotes a growth mindset and student engagement. Challenge Based Learning incorporates the inquisitive elements of PrBL, the authenticity elements of PBL, but does not shy away from the occasionally necessary traditional methods. Challenge Based Learning definitely has a future in my classroom, the trick is, just like with PBL, is how to do it well. Research Methodologies Thoughts - Technology
There are unlimited possibilities for technology in the classroom. Technology can pump up engagement, assist in data gathering and analysis, allow for differentiation and self-paced lessons, open the door to career explorations, and bring something authentic into the classroom. For all the good technology does, it is easy to become a distraction as well. A solid research idea can get sidelined by technology implementation, absorbed by teaching the tech instead of leveraging tech to learn concepts, or bogged down with the details of creating something digitally. Many math projects can easily lose the rigor and depth of content to the wonders of technology. Technology can also become a crutch instead of a tool for students. I considered all these things as I planned my growth mindset and performance task study. The purpose of the study is to examine student’s ability to perform on content-rich tasks, so technology cannot supercede the content. The research also examines growth mindset, so students need to not rely too heavily on technology or it could undermine the mindset work occurring. That said, technology can be incredibly useful for data gathering and, with the CAASPP tests coming up, students can also benefit from developing their tech skills. Some ideas I currently have are self-paced Echo modules, Echo journals, Doc templates in Google Drives, and Google forms. These pieces of technology all help me gather, organize, and store student work for analysis and has the added benefit of easing my students into the upcoming season of online testing. I am also considering using Prodigy, a game based learning system, as a way to track some content specific data. Khan Academy was also up for consideration, due to their growth mindset articles and mastery challenges. However, Prodigy collects more specific data from students and tends to be more exciting for most. I also am considering having students do some independent research, although that is not necessarily a tool for my action research but just an opportunity to leverage technology. My only concern is adding in too many elements. Many technology uses listed above are standard for my room and my site. However, adding in Khan/Prodigy on top of the normal classroom activities (metacognitive journals, growth mindset reflections and assessments, Performance Task practice and scoring) means that I will already have a lot going on. For the sake of my research and data, this may be a time to be frugal with technology implementation. Mathematics is an area of weakness in American education. There is no beating around the bush there. America’s international ranking has dipped significantly in many areas of education, but especially in math. More and more American jobs in the STEM fields are being outsourced to non-Americans. Our school system is not properly preparing our students on a big picture scale. A focus on standardized test performance has not changed this trend. A focus creating formulaic students has not changed this trend. However, some countries, such as Hong Kong, have found success in this approach and consistently outscore American students on international measures. So, it is worth considering that perhaps the mode of instruction alone is not the solution. Perhaps culture and attitudes towards math are worth exploring.
According to NAEP, in 2015, the national average for mathematics scores went down. Concerningly, female students had an overall drop in both 4th and 8th grade. A handful of demographics remained unchanged compared to 2013. Most significant in my eyes, English Language Learners remained unchanged as a group, when both genders experienced an overall drop. Obviously, this data is far to scarce to draw any significant conclusions, but it is certainly interesting to think about. ELL’s did not exactly boast strong scores before the Common Core changes. Are other demographics sinking down to where their scores were? Or is there something in Common Core that is providing a bit of extra support to ELL’s to keep them from sliding? Only time can answer these questions. The only real bright side is that scores are higher than they were in the early 90s. So, we have not backslid several decades worth of progress. However, whether this is a ghostly artifact of NCLB’s obsessive focus on testing or a sign that Common Core is a move in the right direction is unsure. In a few years, when the dust has settled more, we may be able to see some significant data. An examination of the CAASPP results report shows a mild increase from previous years’ results. However, none of them are significant and when you drill down into a deeper demographic breakdown, the meager growth vanishes into a widely varying set of performance levels from different groups. The short of it is, Common Core was not miracle fix people were hoping for. It still holds a lot of potential as a system, but needs time to take root in the minds of students. Common Core is a K-12 system, so it should not be surprise that it is not exploding after only a few years. On an international level, according to TIMSS, 65% of testing is comprised of higher order thinking skills. A student taught to simply follow formulas steps will struggle obtain higher than a 50% a test written that way. Students need problem solving skills and the self-efficacy to engage in them. Students need perseverance to hang onto tough problems. Looking to Singapore, it is instilled in students that they are their nation’s greatest resource. That is a culture that leads to self-improvement, efficacy, and growth. Looking to South Korea, educators are held in high regard. It is difficult to have a high regard for a professional and not also hold their craft in high regard. When education is highly respected, students can find value in pursuing it. It is clear that on an international level, developing positive dispositions towards education in general (and towards math) are prevalent in countries that have high functioning education systems In America, we champion our tech billionaires who never finished college. We idolize celebrities and musicians, in general, who would not be caught dead in a university course. I am may be getting off on a tangent and away from cold, hard data, but it is easy to notice cultural differences between America and the top performing countries in education. Back to topic, California has responded to the need for improvement in education by implementing the Common Core and creating the CAASPP tests in an attempt to steer instruction towards 21st Century Skills. My district has adopted a heavy focus on the 6 C’s via their partnership with the New Tech Network and my specific site has embraced PBL via the Buck Institute and the NTN. Math has certainly lagged behind the curve, but we are now approaching Inquiry Based Learning. As we step up the level of thinking we ask of our students and rise to the rigor and deep, conceptual learning of Common Core and the Mathematical Practices, students will need to develop more grit to be successful. Carol Dweck, and a swarm of researchers following her, have extensively explored the positive benefits of growth mindsets on students. What remains to be seen is how that interacts with Common Core and how it can benefit students on higher order thinking problems such as performance tasks. |
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October 2017
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