I can’t offer concrete strategies or models specific to the AIW framework. However, if “authentic intellectual work involves original application of knowledge and skills, rather than just routine use of facts and procedures” [1, p. 44], then the idea itself seems quite established. The framework, in this sense, appears to be another attempt at organizing teachers’ work in a way that fosters such authenticity. Would you agree?

This leads me to consider a small reframing of the original question: “How do we move forward with implementing a framework for meaningfully engaging with subjects like mathematics, which are often viewed as highly procedural and systematic?”

Such a rewording might make it easier to integrate similar approaches and expand our view of what meaningful mathematics instruction could look like. For example, designing and implementing cognitively demanding, rich tasks could become part of the conversation.

Regarding the framework’s emphasis on “Value Beyond School” or “Connection to the Real World,” I would caution against interpreting this too narrowly. In educational contexts, meaning often begins as a subjective experience before becoming intersubjectively shared. While this may not contradict the AIW framework itself, I wonder if a rigorous implementation could unintentionally suggest that meaning must be constructed solely through the production of something “objectively” valuable. That, in turn, might risk eclipsing the important process of personal meaning-making as a precursor to more generalizable insights.

The question “How can we support teachers in shifting away from traditional approaches?” is central here. In my view, teachers can best support this shift from the bottom up. That means supporting team development, enabling them to collaboratively design learning opportunities tailored to their specific student populations. To make this possible, systems need to provide:

• Resources that create time and space for collaboration and experimentation,
• Encouragement to try new things,
• And support structures that recognize and value efforts before evaluating them.

There are already well-developed concepts for collaborative planning and the implementation of meaningful — and inclusive — math tasks. These exist both in theory and in schools that are willing to experiment. If we adopt a broader perspective, many of these approaches could be seen as part of the same “family” as AIW. In the U.S. context, perhaps they could be described as Dewey-inspired practices?

This kind of framing might also help to identify existing reports of AIW-like practices in math education, along with the associated challenges, learning processes, and professional development efforts that have proven effective.

Of course, international comparisons are not always straightforward. Differences in national education systems — and the fact that many publications are aimed at local practitioners and not written in English — can make direct parallels difficult. Still, one promising and highly adaptable framework from Germany is the “Differentiation Matrix” [2].

This tool supports:

• Collaborative planning of adaptable learning opportunities,
• Centered around a shared learning objective,
• While allowing for a wide range of cognitive and thematic complexity.

The final product of this planning process serves as a framework for students themselves, helping them to find individual and co-constructed learning paths toward meaningful engagement with the common subject. I believe this could align very well with the goals of the AIW framework and might even help to implement it more effectively in diverse classrooms.

References:

[1] King et al. (2009). Authentic Intellectual Work: Common Standards for Teaching Social Studies. Social Education, 73(1), 43–49.

[2] Sasse & Schulzeck (Eds.) (2023). Inklusiven Unterricht planen, gestalten und reflektieren. Die Differenzierungsmatrix in Theorie und Praxis. Bad Heilbrunn, GER.

Thank you @ Joachim Heller for this thoughtful and intellectually generous response. I appreciate the way you've reframed the original question and broadened the conversation to include other pedagogical models and implementation challenges ,especially within mathematics education.

I do agree that the core idea of Authentic Intellectual Work ,as the original application of knowledge and skills, is not new, and that the AIW framework offers a structured, research-grounded way to operationalize these principles in schools. Your reframing of the question to focus on "how we meaningfully engage with subjects like mathematics" , particularly those perceived as procedural ,is incredibly helpful. It indeed opens up space to connect AIW with other established practices, such as cognitively demanding tasks, inquiry-based learning, and even constructivist approaches inspired by Dewey.

Your point about the "Value Beyond School" criterion is especially compelling. I agree that there's a risk in interpreting this too narrowly ,as something that must result in an immediately tangible or socially recognized product. Framing “value” as emerging first through subjective meaning-making (and later becoming intersubjectively shared) resonates strongly with the idea of intellectual engagement as a developmental process , not just an outcome. I’ll be reflecting more on this balance in how I think about and use the framework with teachers.

Also, thank you for mentioning the Differentiation Matrix from the German context. It’s a powerful example of a flexible tool that aligns well with the collaborative planning principles embedded in AIW. I'd love to explore it more, particularly how it supports diverse learning paths without losing coherence around shared objectives.

Finally, I share your conviction that meaningful instructional shifts must be supported from the ground up. Empowering teacher teams with time, trust, and tools ,while creating cultures that value experimentation over perfection ,is essential for authentic implementation, not only of AIW but of any reform that aims to improve equity and rigor.

Joachim Heller

Thank you Taiwo Felicia Taiwo for this splendid phrase:

"Empowering teacher teams with time, trust, and tools ,while creating cultures that value experimentation over perfection ..."

Beautiful alliterations and antithesis wrapped in elegant parallelism -- I am genuinely entranced.

(I hope this does not come across the wrong way -- I truly mean it! I'd love to make a sticker that says: "Empower Teacher Teams with Time, Trust, and Tools, while Creating Cultures that value Experimentation Over Perfection." )

Back to a more sober note -- I'm looking forward to seeing where your epistemological interests will take you. I'm always eager to learn more about other school systems. After all, learning itself must follow some universal principles, since our brains and nervous systems are built on the same foundations. That's why I find it so fascinating to explore which strategies and stumbling blocks are context-specific -- and which seem to be universal across cultures.

Joachim Heller Thank you for this lovely and affirming reply! Your words made me smile , I would absolutely put that sticker on my laptop . “Time, Trust, and Tools” may have to become a recurring phrase in my work.

I deeply resonate with your point about universal learning principles grounded in our shared human neurobiology ,and the tension between context-specific practices and cross-cultural patterns in education. This is a key thread I’m hoping to explore further, especially in mathematics education, where the cognitive demands can sometimes mask the socio-cultural dimensions of learning.

Your openness to understanding other school systems is both refreshing and essential. I, too, find great value in examining not only what works where, but why and how. That’s where I think frameworks like AIW (or the Differentiation Matrix you mentioned) offer such powerful tools ,not as rigid models, but as adaptive lenses through which educators can navigate complexity, tailor learning, and uphold rigor and equity.

Let’s definitely keep the conversation going ,I’d be curious to learn more about the specific ways your work has engaged with these epistemological tensions or how you’ve seen them play out in different contexts.

Count me in, Taiwo Felicia Taiwo :-)

I’m currently working on building a bridge between mathematics education and the programming language Lisp. My intention — or perhaps, more accurately, my hopeful aspiration — is to foster a cross-border conversation. Since national education discourses — especially when related to school systems — tend to be self-contained, I’ve chosen to write in English in order to offer insights into the German context of mathematics education, grounded in a social constructivist stance. My goal is to highlight potential points of connection with similarly grounded educational concepts that may go by different names elsewhere.

This forms the starting point for broadening the lens toward semiotics and eye-tracking studies, with the aim of identifying universal patterns in how we perceive and interpret symbolic mathematical notation.

I then connect this to a brief introduction to Lisp as an alternative symbolic register — one that, I believe, holds promising potential for mathematics education (on, but even more interesting off the computer). In doing so, I hope to bring together communities of committed Lisp programmers and educators in a mutually enriching dialogue.

From a methodological perspective, I’m again stepping across traditional boundaries: I’m using reflexive thematic analysis following Braun & Clarke (2022), not only because it is internationally recognized and respected, but also because it aligns well with the exploratory, interpretive nature of my project. I hope this might also inspire broader adoption of such approaches in German educational research.

All of this is in the spirit of collaboratively engaging with a meaningful shared subject — mathematics and programming — while also mapping out our shared educational ground, both in academia and, perhaps more importantly, in the school setting.