#GMDWrites

NCTM Principles and Standards From an International Perspective: How Does the Curriculum Bring Educators Together on a Common Discourse?

Written by Yeliz Günal Aggül

Curriculum has a very central role in teachers’ lives. Mostly, curriculum is identified with, characterized, and concretized through resources, called “curricular guidelines” in the literature (Pepin & Gueudet, 2014). Their titles might change from country to country. To give examples from two countries where I conduct my research, I can mention NCTM Principles and Standards for School Mathematics (2000) or Common Core State Standards for School Mathematics in the USA and the Teaching Program in Turkey. Regardless of the country in which it is designed and implemented, these resources provide a framework and a national agenda for which learning outcomes will be taught and when. Beyond this central role, curriculum has another, mostly taken for granted, function that has to do with teachers’ solving their problems of practice and improving their teaching. A successfully designed curriculum provides a common discourse that functions as an anchor and orientation that supports teachers in shaping their teaching, finding a path to pursue their professional development, collaborating with their colleagues, and partnering with educational researchers in this process. Ball and Cohen (1999) clearly explain the importance of a common discourse among educators in advancing education:

• In the education of professionals, discourse serves additional purposes, which are related to building and sustaining a community of practitioners who collectively seek human and social improvement. The discourse of teacher education should also help to build collegiality within the profession and create a set of relations rooted in shared intentions and challenges. Such discourse should focus on deliberation about and development of standards for practice and on the improvement of teaching and learning (Ball & Cohen, 1999, p. 11).

1. Although traditional cultural codes of teaching in the US, as mentioned in Stigler and Hiebert (1999), do not cohere with the teaching philosophy that NCTM promotes, the Standards document produces a counter discourse and takes a clear, determined reformist position.
2. NCTM, as a civil organization, provides an effective compilation of research findings on mathematics teaching and learning in this document in an accessible language for those who are not researchers. Being an independent organization of mathematics educators, it functions independently from state bureaucracy, which protects it from political shifts in the country. It also displays a common attitude among mathematics educators who take science and the universal humanitarian goals of education as their points of departure.
3. NCTM has a clear position regarding the pedagogical principles it follows, of which the first one is “equity”, described as “excellence in mathematics education requires equity—high expectations and strong support for all students” (p. 12).
4. It provides a clear outline of how objectives are related from kindergarten to 12th grade, helping teachers have a birds-eye view of the mathematics taught, what their students learn in lower and later grades, and the connections among mathematical ideas. In this way, teachers can make sense of the curriculum, and as a result, they become active agents in implementing and improving this common discourse in practice.

This is not an exhaustive list of the important features of NCTM’s Principles and Standards. My goal here is to provide an international perspective that highlights the significance of these aspects, which are considered ordinary in the daily lives of educators in the United States, and above all, to emphasize how NCTM’s Principles and Standards provide a robust framework for not only mathematics educators in the USA but also as a civil organization that has a universal value that helps to develop a common discourse while improving mathematics classrooms all across the world. Since they did this analysis, our community has appreciated the NCTM’s guide and worked to get a deeper understanding of the vision provided in it. We held long discussions on whether this resource responded to community teachers’ own questions and concerns that they have as practitioners in Turkey.

Designing a curriculum that provides a coherent and robust discourse alone cannot serve as a magical solution to the challenges in education. It is crucial to have effective methods of conveying the intentions of curriculum designers in order to achieve the desired goals. Expecting teachers to simply rely on programs by ignoring their agency should not be the way to disseminate the discourse that curriculum designers wish to share. While a robust, scientifically-based curriculum serves as a starting point for change, implementing systemic changes should also involve teacher learning systems that encourage teachers to actively participate in knowledge building and cultural transformation processes. All stakeholders need to collaborate in developing creative ways of designing participatory professional learning environments, enabling a shared discourse to evolve as teachers engage with curriculum resources and as research meets practice. Only this approach empowers teachers to exercise agency, adapt the curriculum flexibly to meet the specific needs of their students, and take control of their own continuous professional learning.

References

Ball, D. L. & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes and L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). San Francisco: Jossey Bass.

NCTM (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics, Reston.

Pepin, B. & Gueudet, G. (2014). Curriculum resources and textbooks in mathematics education. In S. Lerman (Eds.), Encyclopedia of mathematics education (pp. 132-135). Springer.

Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics: Teaching developmentally. Pearson.

GMD and the Blurring of Boundaries
I can’t believe it’s been around five years since I wrote my first GMD post. It all started when Nate Goza reached out to me, via Grace Chen, about writing for the newsletter. Back then, my role was to summarize whatever was going in the world of math ed, particularly from the standpoint of those on math ed twitter through hashtags like #MTBoS. It was one of my first opportunities to be part of a larger professional community outside of my immediate circle. It also marked the beginning of understanding myself as something I’ll tentatively call a “teacher-scholar”.

The term teacher-scholar might be a loaded term. I use it cautiously because it can connote a teacher who is necessarily part of the formal academy. This is not how I want to use the term. To me, a teacher-scholar might be someone who teaches while also staying interested in professional growth, understanding the sociopolitical aspects of schooling and/or maybe keeping up with academic research. I like to think that many, if not most, teachers can be said to be teacher-scholars. Before becoming a teacher, I was a member of a different professional community: the law. I never vibed with that community, probably because I found myself on the business side of things. After leaving the law, I found myself in a world that felt more like home. Maybe this was because of the scholarly orientation of the job. By becoming a teacher, I could become someone committed to a life of curiosity and creativity. In law, I could become immersed in critical race theory or feminist legal theory. But at the end of the day, I had to go back to the office and give advice to corporate clients based on the same set of statutes and case law. In the classroom, ideas like culturally responsive-sustaining education were not just interesting in their own right; they became necessary for thinking about my role as a teacher, how I interacted with my students, and how I planned for instruction on a daily basis.

This is where the GMD and larger math edutwitter space come in. I learned about ideas like culturally responsive/relevant/sustaining education in these spaces during my first few years of teaching. The ideas of culturally responsive/relevant/sustaining education come from the writings of incredible people like Gloria Ladson-Billings, Geneva Gay, Django Paris, and Samy Alim. But access to these ideas requires an awareness that they exist, and then in many cases it requires digital access to journal articles through a university account (email me for article requests!). The GMD newsletters, webinars, and twitter chats were there for anyone to access. Granted, math edutwitter is an imperfect space and access to the resources it offers is not universal — it is at the end of the day a mostly young-ish crowd, tech savvy, and likely predominantly white, with many “sub-communities” who have thrived in the face of these realities. Nevertheless, the GMD was an incredible place—for me, and hopefully for others—to start to nurture a scholarly approach to teaching that did not require a formal affiliation with the academy.

As it turns out, I ended up pursuing a doctorate in education. 😅. In hindsight, the GMD and math edutwitter bears a not insignificant responsibility for that decision. Being on the inside, so to speak, has allowed me to see in even clearer terms how the academy can be separated from the everyday work of teachers. For structural reasons tied to culture and capitalism, the output and currency of most academic research comes in the form of journal articles. Many of these articles can only be accessed by other academics through subscription access or the purchase of books that are sometimes $100+. Yes, you can and should reach out to authors to ask if they would be willing to send you a PDF copy of their work. But not everyone will, or even can, overcome that interactional friction. Hence, what results is the first and very real wall of separation between the academy and the rest of the world. Elsevier and others, I’m looking at you!

Paywalls are just one aspect of this separation. The language of many journal articles can be obtuse and overly reliant on knowledge of theories and concepts found in other journal articles. To understand X article, you need to read A, B, C theory just to understand what is going on [is academia the original MCU?!]. For better or worse, this might be a symptom of the advice that I received about journal article writing: when submitting an article for publication, make sure it is part of a broader academic conversation. Cite the relevant literature. Keep it under 9,000 words. The result is a potentially wonderful piece of work with terribly dense language that seems to enter an existing conversation mid-stream. The format is often standardized in a way that makes it easier for other academics to read but can be an obstacle for everyone else. Every article seems to conclude with super interesting “more research is required” questions that you may never see or, more likely, may never hear about until three years after those ideas are first introduced at a conference with a $350 registration fee, not excluding hotels, airfare, and food. Oh, and all the articles are only available in English.

The GMD blurred a lot of boundaries. It was a healthy mix of K-12 teachers and university academics, with a leaning toward academics near the end, perhaps as some of us switched over to graduate school. The conversations that folks were having through the newsletter and the webinars were beyond what I was exposed to at my school’s PD sessions. They were deep topics covered at a level of depth that I did not necessarily “grow out of” once I went to graduate school. Ideas like open middle problems, critical data consumption, coded language, and humanizing mathematics have stuck and will continue to stick with me. Even the latest GMD newsletter article–with discussions of concepts like data feminism and black feminist mathematics pedagogies–continues to blow me away. These ideas are being shared in a freely available platform by a team of volunteers. Should people be compensated for their labor? Absolutely. But to the extent that the GMD came together because of folks who were so passionate about their ideas that they wanted to share it in this venue, then what the GMD achieved is absolutely incredible.

🔥🔥🔥

The GMD was a special place to nurture a spirit of teaching-scholarship. It blurred boundaries between the everyday work of teaching and the too often unscalable walls of the ivory tower. I’ll be forever grateful for the opportunities I had to experiment and share ideas. So to anyone reading this, I just wanted to say thanks for everything.
@melvinmperalta

#GMDWrites Again!

Taking Care and Caution with Data Literacy
By: Lizi Metts

Data has become an integral part of our society and culture – from the constant creation of data on mobile devices to the everyday use of data in media and news coverage of current events, politics, and public health. The newfound ubiquity of data opens up opportunities for relevant and meaningful contextual engagement of mathematics using data and data analysis practices and has prompted calls to support students’ data literacy and to modernize mathematics curricula. By ‘data literacy,’ I mean the necessary skills and abilities to access, make sense of, interpret, critique, represent, and ethically use data. As data has become more and more a part of our social world, it’s becoming more apparent that data literacy is important for students – for their lives now and for their futures outside of our classrooms. Data literacy is becoming increasingly necessary for democratic participation as well as economic success, as data is used in a variety of economic contexts and the creation of Big Data careers.

There is a lot of potential here for mathematics education to keep up with these modern needs. Data Science curriculum developers and supporters contrast data science to traditional mathematics learning pathways in which algebra and geometry lay the foundation for calculus. Indeed, there are numerous data science curricula available for teachers to implement and activities like “Data Talks” (think number talks, but with data visualizations) that make incorporating data literacy accessible to math teachers. In my own teaching, I fell in love with teaching statistics. It felt mathematically meaningful but also rich and engaging for my students. I began to incorporate real data into my lessons, whether students were collecting their own data for my AP Statistics class, or I sourced data to create function models for Algebra II and Pre-Calculus, I saw data as an opportunity to make mathematics matter to my students. However, this work was also really complex, both mathematically and socially – finding data, trying to support my students to engage with messier numbers, and opening up discussion about the realities of our social world. My own experience in teaching data literacy has led me to approach the broad and urgent uptake of data science education with a sense of caution.

Problematic Roots in Statistics

1. Examine power – how does power operate in the world?
2. Challenge  power – how can we challenge unequal power structures and move towards justice?
3. Elevate emotion and embodiment – how can we learn and know in different ways, including how we live and feel in our own bodies?
4. Rethink binaries and hierarchies – how are binary systems of counting and classification used to perpetuate oppression?
5. Embrace pluralism – who can we learn from?
6. Consider context – where does data come from? For what purpose was it created? What goals does it serve?
7. Make labor  visible – who were the many hands involved in the creation and analysis of data?

Data feminism is an example of rigorous treatment of data that makes space for and values multiple ways of knowing and takes seriously the social and historical context of data creation and use. This kind of approach makes it possible to marry authentic disciplinary data practices with expansive and experiential ways of knowing and learning.

A more just and expansive approach, however, is not a given. Without care and caution, data literacy can be used to uncritically serve meritocratic and capitalistic goals. Data literacy might make mathematics more relevant or interesting, but to whom and for whom? How important is access and relevance if ultimately, it serves the needs of whiteness while continuing the cycle of oppression? Therefore, we are on the edge of a precipice – to allow data literacy to function as mathematical proficiency has historically, or to take the opportunity to disrupt the status quo and to use data for justice and liberation.

Wisdom I’ve Learned During My Time In GMD

Since 2016, I’ve had the honor to write and curate for the GMD newsletter and present a GMD webinar. I’ve learned much from this community. And for my final submission, I would like to share some.

The unfortunate reality is that we work in a system of math education that values test scores as the ultimate metric of success and progress. But this focus on raising test scores creates math classrooms that reward mimicry, answer-getting, and passive thinking. Students wait to be told what to learn and how to learn it. The focus on test scores diminishes their identity, reducing them down to test scores that need to be raised. This focus also diminishes our own identity and erodes our passion. None of us became math teachers because we’re passionate about raising test scores and training students to be test-takers. We are motivated by more noble calls to action—our vision of equity and seeing all of our students thriving in math class.

Teaching is a craft we learn best through each other.

We work in a system of silos—school buildings, separate campuses, grade levels, bell schedules, and especially our classroom walls. These silos threaten our sense of well-being because we often find ourselves without the collegial relationships and the co-thinking conversations we need to help each other thrive as teachers. But if the GMD has taught me anything, it’s that we are capable of directing our own professional development and we’re capable of becoming active partners in each other’s professional growth.

But only if we’re willing to leave our silos. Which brings me to my last piece of wisdom I’ve learned from others:

Seek vantage—particularly from the student perspective.

By far, the most powerful way to accelerate our own learning is to spend time in other math classrooms. It’s how we can reclaim control over our professional growth and learn how to activate our own sense of agency. Freed from the cognitive demands of teaching, we can begin to shift our perspective on what’s going on in math classrooms. We can watch math class from the student perspective and tap into their experience. And from this vantage in the room, we can see missed opportunities more clearly. And we begin to think of the missed opportunities that may be occurring in our own classrooms.

• How are we showing our students we believe they’re capable? Who is doing the thinking in the room?
• How effectively are we elevating student voices? How are we centering marginalized voices?
• Who holds the authority for learning? How is authority shared with students? How do they have ownership over their own learning?
• How are we valuing multiple perspectives in the room? Do all of our students feel like they belong in math class and have something to contribute?

Let’s teach math together!

I know the Global Math Department reaches far and wide, and geography may work against us. But I’m earnest. Let’s teach math together! And afterwards, let’s share a meal and share some stories about what we’ve learned on our teaching journey. Since November of 2020, I’ve been living a nomad life in my tiny home on wheels called Stoop. And when I can, I love to stop in towns and teach math with folks. You can find out more about that story here.

See you down the road!

Chase Orton
Chaseorton.com
@mathgeek76
@thetravelingstoop

All Good Things Must …

The Global Math Department’s Final Run

Written by Leigh Nataro with Support from the GMD Board
The origin of the phrase “all good things must come to an end,” is not clear. However, the Global Math Department has been a very good thing and now it will be coming to an end. The GMD has helped to provide free quality PD for many teachers over the past 11 years. We will be ending with our last session on May 30th with the amazing math educator and TikTok creator, Howie Hua.

The first GMD webinar “Interactive Notebooks” was held on August 7, 2012 with 17 people in attendance and no email invitations were sent to invite people to attend.  People learned about the webinars the same way I learned about the webinars – through Twitter.  Megan Hayes-Golding organized and led many sessions in the early years of the GMD.  Initially webinars were not recorded for future viewing.  Webinar recordings began in 2014 and some of the recordings were turned into podcasts. Certificates of Attendance were transcribed for live webinar attendance beginning in 2018. To have the GMD reach a larger audience, video recordings of the webinars were uploaded to the GMD YouTube channel starting in May of 2020.

At some point during the pandemic our viewing spiked considerably with multiple webinars having between 100 – 200 people in attendance.  The number of recording views by-passed the number of live views and the most watched webinar recording of all time on our YouTube channel was “Using Delta Math for Distance Learning” by Zach Korzyk with over 5,000 views.  We were truly global with participants from Australia, Canada, Thailand, Turkey, India and Indonesia.

I have enjoyed hosting the GMD webinars over the past eight years and I am grateful to everyone who has contributed to hosting, presenting, booking speakers and writing newsletter content.  Although our formal community sharing via webinars is ending, I look forward to rewatching the webinars on the YouTube channel and continuing to learn and grow from the ideas that have been shared.

The Newsletter Too!

If you’ve missed the Newsletter this year, we’ve missed you too!

The first ever GMD Newsletter was sent out on April the 28th 2014. You can see it here! Shout out to the original subscriber, admin, and editor Michael Pershan! For 8 years we continued to put out a weekly (and eventually biweekly) Newsletter highlighting the goings on in the intersections of the math, education, and math education worlds. Our subscribership grew from one to nearly 2,000 during that time with nearly 20% of our subscribers from outside of the US. It was a great run and we thank all those of you who read and grew along with us. #GMDWrites!

We our planning to put out a few more editions of the Newsletter as we celebrate the end of the GMD’s fantastic run. As always, we are hoping to get some contributions from our readers and folks who have attended the Webinars. See the announcement below if you are interested!