Tag: innovation

What does math classroom innovation look like now?

If you don’t come from an education background, the concept of a student-centered or discussion-based classroom can be confusing to you, especially when it comes to math. Your idea of a “good” or “rigorous” math class might be one that is traditionally teacher-centered and requires a passive stance from students. Even many educators haven’t been exposed to the latest educational research, recent pedagogical initiatives, or the need to support greater neurodiversity. Every school should prepare to have, and to revisit regularly, the conversations about what best suits their school’s idea of an innovative mathematics program. Those conversations will form the foundation of curricular commitments and changes in teaching practices, in support of our shared values about the subject of mathematics.

The Innovative Math Classroom of 2024

What does today’s innovative math classroom look like? Is it an abundance of technology use, including AI for student learning? Is it students seated in groups doing explorations of traditional mathematics topics?

I would say that it can be seen from this perspective, but the innovation that needs to occur is even more basic than this. As AI becomes more and more normalized in student work, it will be more important than ever in the classroom to filter out the parts of mathematics that are redundant or procedure-based. Instead of factoring complex polynomials in an Algebra II class, students should understand the reasoning behind what factoring tells you about the polynomial and why it’s important. An innovative classroom will value the parts of mathematics that allow for higher order thinking – deciding on strategies, comparing, conjecturing and critiquing different processes.

Understanding the processes and procedures of what most people consider “math” today will be superseded by critical thinking and overarching reasoning skills. Mathematics will be the topic for the study of writing algorithms and engineering prompts for AI. It will become the discipline of study for scholarly communication with artificial intelligence.  

As AI becomes more and more normalized in student work, it will be more important than ever to filter out the parts of mathematics that are redundant or procedure-based.

Leading Towards an Innovative Math Program

How do schools decide to innovate in their mathematics program? How do they identify where the program is in the transition to an effective, innovative math classroom? 

First, teachers must be aware and supportive of making change – changes to what texts they use, their familiarity with support services for students, and incorporating updated pedagogical practices that enhance and value specific higher-order student thinking skills. Students need to be taught how to become better mathematical communicators, and how to present mathematical ideas in a clear and engaging way for their peers. Instead of a classroom where students sit passively – asking questions of the teacher that only relate to their individual understanding of a problem –students should be more actively doing mathematics, conjecturing with peers and judging for themselves which problem-solving methods are optimal in different circumstances.

Next, a deep and rigorous curriculum review of the mathematics program needs to be complete for all grades. Here, we seek to discover whether there is alignment between curricula for lower grades, middle grades and upper grades. Are learning outcomes and prerequisites clearly outlined for each course in the sequence? Are teaching practices aligned so students have similar experiences in their courses across the program? These are the types of questions that a department chair or academic dean should consider before attempting to make changes in innovation.

Evolve Your Math Programming

All change comes with trepidation and consequences in the community. Teachers will need professional learning, and students will need help accepting different methods of instruction. However, reinventing a school’s mathematics program is essential to remaining relevant and innovative. These ideas are the future of mathematics education and should be explored to keep a school’s mathematics program modern and creative.

originally posted on the blog of Aptonym 

Mathematics Curriculum in the age of AI – What can humans do?

It’s 1976 and I’m in Mrs. Gerber’s second grade classroom. After learning our times tables by heart (I was so proud), I’m sitting at my four-table group and Mrs. Gerber comes over handing out something small and square with buttons that looks really cool. She introduces us to the four-function calculator and while lots of other students are seeing what they can write with numbers upside down on the small screen, I am plugging in the biggest numbers I can think of and seeing what the product would be. When will it be too big for the screen? What will it tell me? Is there a pattern in the numbers?

I was able to come up with some questions that Mrs. Gerber hadn’t even thought of, and it was all because of this new toy that I was able to play with in class. Times have definitely changed since then and the “toys” that students play with in class currently, were probably unimaginable in 1976. However, one thing still rings true: that playing with those toys changes everything.

As a math teacher since 1990, I have seen many phases of technological change in education. I remember learning how to use the TI-83 calculator for the first time and thinking of the wonderful ways that this would change the way I taught. So many questions existed about what was important and what was not to change or retain in the curriculum.

We are once again at a crossroads – one that math education has seen a number of times – where we as a group (or often individuals) decide the importance of specific topics that are “covered” in our curriculum. This autonomy given to math teachers often varies from district to district, even school to school – especially in the independent school world. The eternal question that math teachers do not have enough time to “cover” the contents of the textbook has now come to another moment – What can we leave out and still call ourselves math teachers? Still call our learning outcomes mathematics? The advent of AI should make us all think about what we as mathematicians and educators, think teaching math should be about. AI can serve as tutor, assessor, colleague, student peer and many other roles. What is it we’d want to get out of that “relationship” with the AI?

Personally, I have been contemplating this for a long time and I still come back to the curriculum. There’s so much at this point in education that is extremely intertwined and hard to untangle:

• Working with digital natives for whom technology may not be the best of devices to be interacting with

• The risk-taking and being wrong that students today are mostly lacking

• College admissions dependency on an age-old tradition of racing to Calculus

• The phenomenon of the ‘snowplow’ parent who seeks to remove all obstacles and suffering from a student’ pathway

All these issues affect the way we look at curriculum for mathematics education. Many say that too much access to technology undoes all the skills that may have laid the foundation of students’ mathematical understanding. Others say that students will use the technology as a crutch and not truly “learn” the skills they need or learn from their own mistakes. Teachers will cite the necessity for certain traditional skills based on students’ need to be able to take Calculus by grade 12. Parents will create the obligation of the school to allow students to use AI for homework since the expectations of the school or teacher are “too high.”

It is always important at these crossroads to consider the skills that students learn through the curriculum. What are our goals for teaching factoring? Finding horizontal asymptotes for rational functions? Simplifying complex rational expressions by hand? Memorizing SOHCAHTOA? Why do we teach these skills? If the purpose or answer is so that students can do math “in their head” or “on their own”, my response to this is that eventually this will no longer be required. What we’ve wanted as math teachers as far back as 1990 (and probably further) and what mathematics researchers like Carpenter, Fennema and Schoenfeld have been promoting is “teaching for understanding” or “making sense” of mathematics.

We as a community need to grapple with the question of what is most important to understand and how what we as humans are capable of will be more than what an AI can “understand” for us. Creating a holistic view of teaching mathematics means to dive into the new world of AI and look at the understanding and skills students see as “mathematics” while at the same time considering the new possibilities of what math can be. Instead of factoring, solving, using, “plugging in”, perhaps we change the curriculum so that inquiring, critiquing, deciding and evaluating are the ideas that come to mind when students think of math with AI? Could empathy, discussion, collaboration and abstraction be the main learning outcomes of mathematics education since so much can be done with AI now?

Contemplating these possible futures takes courage, knowledge and experience. I am sure that as a community, we will eventually get there. We will continue to have students that will want to write “hello” upside-down on their calculator (or other words!), but we will also have that students that push the AI to see what they are capable of. We can change what we teach in the mathematics classroom to encourage all students to experiment with curiosity and to help us shape the future.

Be the Change You Want to See

I just finished listening to a great “blogcast” that Tony Wagner gave as an interview for Blogtalkradio about his new book “Creating Innovators:The Making of Young People Who Will Change the World.” Kind of a neat idea for a book in which he has done some great research looking into how some new ideas got started by young people, how their creativity was fostered in their childhood, parenting and education, etc.  Definitely worth taking a listen to.

Listen to internet radio with Steve and Mary Alice on BlogTalkRadio

One of the things that Prof. Wagner talks about in his interview is the idea of fostering the creativity that leads to innovation.  As he spoke to these great innovators that he interviewed, they could all name at least one teacher in their career who had a “significant impact” on their learning.  Interestingly, the characteristics of that teacher were often very similar, Wagner said.  They were known for encouraging collaboration and often assessing it, creating a classroom that was often interdisciplinary and problem-based (of course) and empowered his or her students to be creative in their problem-solving and make mistakes.  Why is this not surprising?  To all of us who strive to foster the practice of creativity and hope to allow our students to become innovative and original thinkers, we have known that these are the values that we should uphold in the classroom. I’m so glad that Wagner did this great research and wrote this wonderful book.

However, we also know the realities of the limitations that many of us teachers have that come with the system within which we teach.  I have spoken to so many teachers from around the country who, with all good intentions are striving to make their classrooms more problem-based and encourage creativity.  They are truly trying to be the change they want to see in mathematics education today.  But the fear of standardized testing that is not assessing these values, affecting their evaluations or public awareness of parental or administrative dissatisfaction or vocal disagreement with these goals, needs to be balanced with a teacher’s desire to move ahead.  Limitations of a teacher’s time, energy and their own creativity keep them from being able to proceed without support from like-minded colleagues and leaders in their district.

At the end of the interview, Prof. Wagner talks about his move from the Harvard GSE to his new position in the Technology and Entrepreneurship Center at Harvard.  He says something like he’s found that he doesn’t belong in a school of education because he’d like to be somewhere where the focus is “explicitly on innovation.”  My question is why can’t that be a school of education? or a school at all?  Why can’t learning be explicitly innovative and thought about as innovation in general? I believe all of us are capable of thinking of our schools as places of learning where students are being innovative as they learn.  Every day I ask my students in my classroom to attempt to think of something new to them.  It may not be innovative to me, but as long as it is in their eyes and their brain is attempting to see something in a new way on their own, I believe they are being innovative.

I would encourage us all to continue to be the change that we want to see in schools and not try to find other places where we think we belong.  It’s so important that we continue to make these changes no matter how small and I hope to continue to be a resource in your own classroom innovation!