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5/16/2024
Foundations of Math EdUCATION
I have spent the morning reading and posting on various platforms about the state of mathematics education in America. Amidst the ongoing debate concerning the influence of #AI and its potential impact on math instruction, I find that many arguments tend to overlook the most critical issue at hand: the pervasive lack of deep understanding that continues to hinder both students and some educators in our mathematical culture.
Our educational groundwork seems precarious, akin to a structure built on shifting sands. While newer instructional technology offers an opportunity for fostering profound engagement with mathematical concepts, for now, it often falls short, reduced to mere tools for rote practice and mundane tasks in many mathematics classes. This approach neglects the rich problem-solving experiences essential for our students' mastery of mathematics. Consequently, math classes become not only tedious for many students but also seemingly detached from the broader context of life, academic pursuits, and genuine education.
To address the shortcomings in mathematics education, we must first reinforce our foundational philosophy, emphasizing the importance of quality teaching and purposeful learning. The ongoing debate between direct instruction and inquiry-based methods merely hints at the cracks in our educational foundation.
It is disheartening to observe the lack of genuine efforts within higher education and institutional settings to fortify this foundation. Instead, we find ourselves entangled in a transactional system, where schools seek solutions, often through financial means, only to be served with temporary 'fixes' that offer no substantial improvement over previous iterations.
True progress in mathematics education necessitates a concerted effort toward building stronger foundations. There's no shortcut or quick fix to achieving this goal. It demands a collective commitment to fostering meaningful learning experiences and empowering both educators and learners to engage deeply with mathematical concepts, ultimately paving the way for a more robust and enduring educational landscape.
What are your thoughts about the use of AI for math education?
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Susan Carriker
NEWS and TRENDS
A new study commissioned by the Dutch government raises concerns about the potential for algorithmic bias in educational technology. The research released on Monday suggests that learning systems that make use of artificial intelligence (AI) can put some groups of students at a disadvantage even though the systems are intended to make education for personalized.
The study examined how algorithms are used in both primary and higher education, the Netherlands Institute for Human Rights said. Researchers found that many schools utilize adaptive learning systems, which automatically adjust exercises based on student performance. While these systems can provide targeted support, they may also reinforce existing biases when poorly designed.
“Unfortunately, prejudices about groups of students already play a role in education,” the report stated. Students are already more likely to receive lower initial school recommendations despite their test scores when they come from lower-income families or if they have a background including parents or grandparents who immigrated to the Netherlands. AI systems that are not rigorously tested on diverse student populations risk amplifying these inequalities.
Before she got to the math in her lesson on linear equations last fall, Sydney Kealanahela asked her class of eighth graders on Oahu why kalo, or taro root, is so important in Hawaii. What do you know about kalo, she asked them. Have you ever picked it?
A boy who had never spoken in class, and never seemed even slightly interested in math, raised his hand.
“He said, ‘I pick kalo with my grandma. She has a farm,’” Kealanahela recalled. “He was excited to tell us about that.”
Class discussion got animated. Everybody knew about poi, the creamy staple Hawaiian food made from mashed taro. Others had even noticed that there were fewer taro farms on Oahu.
That’s when Kealanahela guided the conversation to the whiteboard, plotting data on pounds of taro produced over time on a graph, which created a perfect descending line. The class talked about why there is less taro production, which led to a discussion about the shortage of farm labor.
Kealanahela had taught eighth-grade math for six years at a campus of the Kamehameha Schools, but this was the first time she had started a lesson with a conversation about farming. The idea came from professional development she’d just completed, in ethnomathematics, an approach that connects math to culture by embedding math in a story about something relevant to students’ lives.
Ethnomathematics isn’t new, but until recently it was limited to a niche area of educational and anthropological research on how different cultures use math. Over the past couple of decades, it has evolved into one of several efforts to create more engaging and inclusive math classrooms, particularly for Black, Hispanic, and Indigenous students, who tend to score lower on federal tests than their Asian American and white peers. Ethnomathematics advocates say that persistent achievement gaps are in part a result of overly abstract math instruction that’s disconnected from student experience, and that there’s an urgent need for new approaches that recognize mathematical knowledge as it’s practiced outside of textbooks.
Many Black and brown students don’t feel comfortable in math classes, said Shelly Jones, professor of math education at Central Connecticut State University.
I’ve made no secret of my fervent belief that curriculum is the overlooked lever in education reform. Replacing the slapdash, incoherent, and under-nourishing mélange of materials to which the typical U.S. student is exposed with a more rigorous and thoughtfully sequenced student experience holds promise unmatched by the “structural” reforms favored by policymakers. Over the years, I’ve also crossed swords occasionally with fellow curriculum advocates who labor under the misconception (or allow others to do so) that simply adopting high-quality instructional materials (HQIM) is a magic bullet, or who obsess over minor points of orthodoxy between programs. The larger battle to be fought and won is making curriculum—virtually any decent curriculum—central to school improvement efforts.
In fact, I’ve lately struck from my vocabulary the phrase “curriculum adoption” in favor of curriculum purchases. The word “adoption” implies a much higher bar than just forking out taxpayer dollars for a new program and calling it a day. It’s a serious and sustained effort shared within and between grades to implement curriculum rigorously and with fidelity. Such efforts remain the exception, not the rule. Thus, I’m pleased to recommend a new case study published by Rivet Education, a curriculum-focused consulting group, which lays out the steps needed to turn a curriculum purchase into an adoption process worthy of its name, and that moves the needle on student outcomes.
In 2018, teachers and leaders in Wisconsin’s Mount Horeb Area School District made the decision to adopt a new math curriculum called “Bridges in Mathematics” and produced by The Math Learning Center. Students in this small town in southern Wisconsin were doing reasonably well on state math tests, but teachers had noticed that they “struggled when given more challenging math work” including problems that required them to conceptualize, explain their thinking, or apply math to real-world situations. Mount Horeb embarked on a multi-year “journey” to fully implement Bridges.
TPC Desmos Calculator Training
Susan Carriker
Retired Math Teacher, Math Teaching Specialist, Assessment Writer, and #EdTech Trainer.
↓ Older Blog Posts ↓
5/9/2024
NoT Your Typical Math Teacher
I am not your typical math teacher. My journey to becoming a teacher took a few detours and nearly ran off the rails before it got started. When I reveal that I started out with a D in 6th grade math, flunked out of my first calculus course and earned my first college degree with less than a 3.0, I start to notice that awkward silence, perhaps it is pity, but what these experiences have shown me, is that I survived a system that was actually trying to keep me out. In spite of every hurdle in front of me, I just kept going. I even wormed my way in where I was not invited (more than a few times) and revolutionized a few systems along the way, but I have never forgotten how easy it would have been to just walk away.
If you haven't already read my story (I have a free e-book posted on the Training Center page), you may want to know more about how I got here, but for now, I just want to encourage you to reject the naysayers and just keep going. Maybe you are coming through a teacher prep program, or maybe you are already in the classroom, but you just feel like maybe you don't measure up. Those lies are told every day. Sometimes we tell them to ourselves, but more often, we 'hear' those lies through the condescending tone from other educators. Maybe a professor made you feel 'less than.' Maybe you didn't come from a family of influence or wealth. Whatever may have gotten in your head about your worth, I can assure you that none of those things determine your worth. What they don't want you to know is mathematics classes are full of kids and adults that have these feelings. Perhaps it is the reason so many kids and adults have negative ideas about mathematics.
No matter how accomplished I may have become over the years, I will never fit the mold of a typical math teacher. I will never 'fit in,' but that is actually a blessing. My pioneering spirit has enabled me to go to more places, accomplish more and actually rescue quite a few kids along the way who were languishing in a rigid system that often fails to acknowledge or appreciate their brilliance.
Let your differences be your greatest testimony. Kids and adults need to hear that you have struggled, that you have learned and that you have evolved over the years. As much as we like to appear picture perfect, no one is. I encourage you to share your story with your students and other educators. We are all in this together.
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Susan Carriker
4/29/2024
It is time to ask the experts
The education sector is currently witnessing a fervent embrace of artificial intelligence (AI) technology, with tech companies racing to develop innovative solutions for teaching and learning. Understandably, this AI craze has led to a flurry of activity, as every major educational company seeks to integrate AI applications into its business model. However, amidst the excitement and hype, it's essential to pause and consider whether these advancements truly meet the needs of those directly impacted: teachers and students.
Despite the proliferation of AI-driven gadgets, chatbots, and applications touted as educational game-changers, conversations with educators reveal a stark reality: little has fundamentally changed in the classroom. This disconnect is not new; it echoes previous cycles of EdTech booms, where the voices of teachers and students were often sidelined in favor of technological innovation. The common thread running through these cycles is clear: meaningful progress in education cannot occur without the active involvement of those who ultimately implement and utilize these tools.
Teachers are the frontline implementers of educational technology, while students are its primary users. Yet, all too often, their perspectives are overlooked in the rush to innovate. Without meaningful dialogue with educators about what works and what doesn't in the classroom, the promise of revolutionary change remains unfulfilled. Similarly, failing to engage with students risks deploying technology that hinders rather than enhances learning outcomes.
Reflecting on past attempts to revolutionize education, like video lectures, can offer valuable insight. The initial excitement surrounding video lectures (back in the 70s and 80s) as an educational panacea quickly waned when teachers observed students disengaging and even falling asleep during passive viewing. While platforms like Khan Academy have evolved to incorporate interactive elements, the lesson remains clear: technology alone cannot drive meaningful change in education. Instead, it's the thoughtful integration of technology with pedagogical best practices (and student engagement) that yields positive outcomes.
To truly revolutionize education, whether through AI or any other emerging trend, it's time to prioritize the voices of teachers and students. Billions of dollars are invested annually in educational research and technology, yet many initiatives falter due to a lack of genuine stakeholder involvement. By giving teachers and students not just a voice but a choice in the adoption of new systems, we can avoid costly missteps and ensure that innovation aligns with real-world needs.
In an era marked by unprecedented challenges in education, it's imperative that we turn to the true experts: teachers and students. By fostering a culture of collaboration and inclusivity, we can harness the transformative potential of technology to create authentic learning experiences.
What are your thoughts about this latest AI craze? Join the conversation.
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Susan Carriker
4/21/2024
DO Reformers Always Fail?
Recent debates over reform in math education (as espoused by Jo Boaler, Peter Liljedahl, Conrad Wolfram, and many others) reveals a commonality with reformers vs. the status quo throughout history. Reformers always lose initially.
When battling generations (even centuries) of norms, there will always be backlash from some in society, and the loudest critics will usually hail from the majority class who have historically benefitted from the status quo. Inevitably, reforms are tabled (or dismantled) as public outcry intensifies. It is exceedingly rare for reform (of any kind) to be enacted quickly or to last (at least initially) in the face of such intense opposition. In fact, most reformers do not live to see many of the reforms they have inspired. Let's take a quick look at some of the reformers in history that set the wheels in motion, but did not live to realize the fruits of their labor.
Nicolaus Copernicus (1473–1543)
Copernicus (Polish astronomer) suggested that the Earth and the other planets revolve around the Sun. This (heliocentric) model challenged the prevailing geocentric model, which placed the Earth at the center of the universe. His ideas faced significant resistance and ridicule from both the religious establishment and the scientific community of his time. It wasn't until the late 17th century and early 18th century that the heliocentric model began to be widely accepted within the scientific community.
Martin Luther King Jr. (1929–1968)
The iconic civil rights leader played a pivotal role in the American civil rights movement of the 1950s and 1960s. His efforts led to significant advancements in racial equality, including the Civil Rights Act of 1964 and the Voting Rights Act of 1965. However, King was assassinated in 1968, just as the movement was gaining momentum and some of his dreams were starting to be realized.
Mahatma Gandhi (1869–1948)
Gandhi, the leader of the Indian independence movement against British colonial rule, advocated for nonviolent resistance and civil disobedience as means to achieve social and political change. His efforts eventually led to India's independence in 1947, but he was assassinated in 1948, just months after achieving this milestone.
Suffragettes (1848–1920)
Countless women fought for "the right to vote" around the world, including figures like Susan B. Anthony, Elizabeth Cady Stanton, Emmeline Pankhurst, and Alice Paul. While many of them saw progress toward women's suffrage during their lifetimes, some did not live to see the full realization of their goal in their respective countries.
Abraham Lincoln (1809–1865)
Lincoln led the United States through its Civil War and issued the Emancipation Proclamation in 1863, which declared that all enslaved people in Confederate-held territory were to be set free. However, he was assassinated in 1865, just as the Civil War was coming to an end and before the passage of the 13th Amendment, which formally abolished slavery in the United States.
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Advocating for reform in mathematics education and challenging the status quo will be met with resistance, especially from established institutions and entrenched traditionalists. It's crucial to recognize that mathematics, like any field, must evolve over time. Those who were once excluded must now be invited to participate.
Supporting reform efforts aimed at making mathematics education more accessible, inclusive, and relevant to diverse learners is vital for building a society where everyone has the opportunity to enjoy mathematics and contribute to its advancement. It requires courage, perseverance, and collaboration to challenge existing norms and advocate for change, but the benefits of a more equitable and inclusive mathematical community are worth the effort.
I encourage you to join the fight.
Who else should be added to the list above? Join the conversation.
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Susan Carriker
4/16/2024
Test Prep Reflections
Over the past couple of months, I've been diligently producing materials and videos, driven by the ongoing test prep season, which is now in full swing across most states. I've discussed my reasons for engaging in test prep in my last blog post, so I won't rehash that here. However, I've gained some insights into the differences between state assessments, particularly in Algebra 1 EOC assessments, which I'd like to document here for those interested in knowing more about these tests.
Mississippi (MAAP)
Completing the #MAAP series was the easiest because I was already familiar with the test (I have worked as a writer and reviewer for Questar/MDE for several years). Even though I had a large collection of test prep materials created for MAAP, I still needed something new to align with the updated blueprint, so I created teacher training videos and extra practice sets to update my collection. Navigating the Mississippi test system (now a part of NWEA) was remarkably straightforward. While the navigation bar being at the bottom was a minor inconvenience, the overall interface was very user-friendly. The Desmos calculator, with its flexibility and full functionality, was a standout feature. This was not an adaptive test, which made navigating to particular questions easy. This was my favorite test to prep.
Texas (STAAR)
Despite Texas being home to tech giants, the #STAAR test proved challenging to navigate. The interface was subpar, and the calculator functionality was the most limited (sliders, inequalities, implicit equations and more are disabled). The calculator was also very challenging to resize or move. Additionally, because it was an adaptive test, it restricted skipping ahead, and the level of tedious manipulation required for many problems was excessive, potentially detracting from students' comprehension. This was my least favorite test to prep.
Louisiana (LEAP)
Prepping for #LEAP was a generally a positive experience. The test's simplicity and intuitive navigation were commendable, although the inability to resize the calculator posed occasional challenges. The quality of test items, particularly in assessing conceptual understanding, was noteworthy. The calculator had nearly 100% functionality. This was not an adaptive test, so moving around the test was easy. Despite these merits, accessing LEAP materials on their resources page proved to be a nightmare. The practice test and other test materials (blueprints, item specifications, etc...) were very hard to locate.
Georgia (GMAS)
The #GMAS assessment was decent, with an interface that is almost identical to Louisiana's LEAP. However, the excessive volume of text and verbosity in questions may disadvantage students, particularly those with language difficulties. While the calculator functionality was reasonable, not all features were enabled. This was not an adaptive test, so advancing through the test was simple. The difficulty of the items (DOK) seemed a bit lower, although reasonably aligned to the Georgia standards.
Arkansas (ATLAS)
My experience with #ATLAS was limited, but my initial impressions were mixed. The test interface mirrored Texas', which posed usability challenges (the calculator had the same issues as Texas). Additionally, the test's rigor, particularly in its open-ended questions, seemed excessive for 8th or 9th grade students. Despite some redeeming qualities, such as a few well-crafted, interesting questions, the limited calculator functionality (implicit equations were turned off) and the number of steps needed to complete certain tasks, detracted from its overall effectiveness. This was a fully adaptive test (no skipping questions). In general, this was the most challenging test to prep.
In an ideal scenario, these tests wouldn't exist, but until then, my aim is to equip students and teachers with the necessary tools to navigate them as seamlessly as possible. Recent news suggests Mississippi may eliminate the Algebra 1 MAAP assessment, potentially influencing other Southern states. Only time will tell.
If you have questions or would like to share your thoughts on these assessments, feel free to connect with me on Twitter and join the conversation.
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Susan Carriker
3/28/2024
Why do I do Test Prep?
If you follow my Twitter stream you will find test prep resources right alongside articles and tweets deriding the evils of testing and other barriers to education. It may seem contradictory to engage myself with activities that seemingly support the use of standardized testing and multiple choice exams in school, but there really is a simple explanation for why I choose to prepare kids and teachers for state and national standardized tests. Kids and teachers are stuck in a system that punishes those without access. These tests currently are used to measure kids and teachers and often block access to those who perform poorly. I don't like these tests, but I do like teachers and kids. I choose to help both as best as I can.
If you are poor or a minority student in America, the probability of you having a math teacher that uses instructional technology to its fullest potential is quite low. If you are a teacher working in a school district that is located in an area of the country that is poor or underprivileged, you may find it difficult to know how to begin acquiring and learning about the newer instructional technology if you don't already have a strong support system (#PLN) or knowledgeable colleagues to guide you in the right direction.
There is free training on just about every imaginable #edtech platform available online at low or no cost, so I am not saying that Tech Know Math is alone in this universe of math #edtech training, but I do have a unique perspective in many ways because my aim is to equip those who may not otherwise be equipped. I want to engage with learners who are turned off by traditional classroom practices. I want to inspire math educators who are frustrated with their jobs and ready to try something new.
The videos I have created for kids are designed as tools to help them get over the barrier of testing by knowing and using the tools in the Desmos Calculator. Kids who have no money for tutors and expensive calculators can now learn (for free) in my student facing videos about the strategies that can make very challenging math concepts seem simple! The free videos and paid materials I produce for teachers give them access to better quality resources at a tiny fraction of the cost charged by some of my former colleagues. I once worked for a company that charged $750 for a 4-day training (and that didn't include travel, lodging or food). The cost to attend many educational conferences can top $1000 when you factor in travel and other expenses.
Living on retirement income is no cakewalk in this economy, so that is another reason I do what I do. I try to give away something every week in my store to those who can not afford to purchase curriculum materials, but I do charge for nearly all new major assessments that I create. The reason? It is my only supplemental income now, and it also helps keep the tests I have created from being downloaded and copied by too many. Assessments behind a paywall are protected from excessive exposure which helps keep them more reliable.
Ironically, some of the same people who hop on planes to go to educational conferences to dole out thousands of dollars to receive and deliver training sometimes find fault with my methods, but, the ones who will never be able to afford those conferences deserve access to #edtech skills and quality resources, too.
Hopefully, I can continue to provide training and quality resources for a long time to open up the doors of access for those who have been shut out in our current system.
I welcome your input and suggestions.
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Susan Carriker