Learning

Teachers look at student work often and for many purposes. Many look individually, as a way to better understand student thinking and to inform instructional choices. Other times, looking at student work may be collaborative, such as when co-teaching, during a professional learning meeting, or as part of an instructional, curricular, or school reform decision-making process. These types of collaboration often take place after student work is completed and when students are not present. The Math for All approach combines aspects of both individual and collaborative ways of looking at student work by including planning and debriefing with colleagues and an emphasis on an observation process for looking at a student at work—attending carefully in real time to one student and their ways of learning.
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Recently, I’ve been reading a bit about AI—artificial intelligence—the technology that is supposed to change the world as we know it, including the world of teaching. The changes are anticipated to be so momentous that the President issued an executive order to make sure that the development of AI is “safe, secure, and trustworthy.” In the world of education, students are already using AI to do their homework. After all, it can write papers, analyze texts, and solve problems. Some even say that AI might eventually make teachers obsolete. That certainly hasn’t happened yet, and while AI tools can help students cheat, they also have the potential to help them learn and help their teachers develop better lessons that deepen learning.
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How often do we ask students to show their mathematical thinking or explain an answer using words, pictures, or diagrams? If you’re like most of us, the answer to that question is probably “Very often”! But what does it mean to express mathematical ideas and processes through these modalities? What is our expectation that students’ work contains language that connects to diagrams and pictures? Are representations of thinking created after a solution is found, or are pictures, diagrams, and language part of developing a solution? To explore these questions, let’s first take a close look at four mathematical tasks, each requiring increasingly complex conceptual understandings, and the visual representations and language that can support understanding these tasks.
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October is designated as Celebrate the Bilingual Child Month, and we take this opportunity to recognize and celebrate all the strengths that multilingual children bring to the classroom and to highlight some practices that can support these students in math. In the United States, about 10% of school children are English Learners (ELs). It’s important to note that EL refers to students who are in the process of gaining English proficiency but does not include the millions of students who are bilingual or multilingual and have gained English proficiency, having formerly been classified as ELs. ELs are a diverse group of students, representing many different school experiences, languages, academic strengths, cultural norms, and more. In this blog, I will refer to multilingual learners in recognition of the many students who speak two or more languages and who may be current or former ELs.
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While playing Monopoly with my 5-year-old, I gave him a $100 bill to pay $12 in rent. He wasn’t exactly happy, but he figured out that he owed me $88 and then figured out how to make that amount with the available bills. Several years later, while walking through the forest, my 7-year-old daughter looked down at her feet and said, “I wonder how many steps I’ve taken in my life.” After a few silent shouts of joy upon hearing her curiosity, I replied, “What a great question. How would you figure that out?” Fast forward to a few days ago, my 10-year-old son was grocery shopping with me. “Can we buy this bag of pistachios?” “We don’t need pistachios,” was my reply. “Ple-e-e-ease?” accompanied by puppy dog eyes. “Okay, but get the small bag.” “The big bag is a better buy,” he replied, “because, look, this one is 8 ounces for $6, but the bigger one is twice as big for only $9, which is less than twice the price.” We went home with a big bag of pistachios.
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With the abundance and depth of knowledge gaps created over the pandemic years, many educators are turning to new curricular resources to help meet students’ diverse needs. However, there is much to consider before choosing a resource. Per the company Education Elements, “Curriculum selection is no longer about textbook adoptions that happen every few years. Districts today are developing a strategy for instructional materials adoption and selection that takes into account district goals, pedagogical shifts, cultural relevance, and student-centered environments.” But before jumping into something new, let’s take a step back, and consider these four steps to help guide our curriculum decisions, focusing on mathematics resources.
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Do your students seem less enthusiastic about working in math groups or communicating their ideas and thoughts in class? If so, you are not alone. Teachers with whom we work are observing a decline in students’ skills to work together and express their thoughts. What has been the impact of the COVID-19 pandemic on students’ discourse? A great deal has been written about the impact of the pandemic on student learning, standardized assessment results, and students’ social skills (Mervosh & Wu, 2022, Associated Press, 2022, Campbell, 2021). However, little has been written about how students’ ability to communicate their mathematical understandings has been impacted. Anecdotal evidence suggests that the COVID-19 pandemic has impacted students’ abilities to develop mathematical discourse with their peers and communicate their mathematical understandings. This post will provide explicit structures and routines that can be used in classrooms to develop students’ ability to engage in productive mathematical discourse.
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“When am I ever going to use this?” We, the authors, have been talking about math education since we met eight years ago, and trust us, this is not an easy question to field. Teachers can’t really predict which mathematics problems a student will face, so the quick answer has become, “In the future you’ll come across a problem and “presto” you will see the relevance of this bit of information.” In all fairness, while this is a time-saving response for the teacher, it does not address the real issue, which is “Why does the American student ask this question in the first place?”
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Everything I had thought about coaching in education changed when I read the article “Personal Best” by Atul Gawande several years ago. In the article, we learn that eight years into his surgical career, the author felt his surgical skills had plateaued as compared to the steady upward growth he experienced during the initial launch into his professional work. And so he asked a former instructor to observe him during surgical procedures and serve as a coach. He shared that the first procedure he did while being observed went incredibly smoothly. Or so he thought. His coach provided two pages of “small things” that, from his coach’s vantage point, affected his work in ways that offered opportunities for improvement. The coach pointed out that shifting his arm or foot position could offer greater stability while working. He noticed how the surgical light moved during the procedure, thus changing the amount of direct light shining on the wound. These “outside eyes,” as Gawande described it, along with several months of continued observations and follow-up conversations, offered Gawande the chance to get better at his job.
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Think of a situation where you felt you belonged. What was that like? What made that happen for you? Consider a time when you sensed that you didn’t belong. How did you feel? What made you uncomfortable? And what do these questions have to do with teaching and learning mathematics? You will find out in this blog.
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