There’s a scene from The Matrix which I absolutely love as a metaphor for the choices we make and the ignorance we can choose to turn on or off as it suits us. Watch the scene or read the dialogue below. Morpheus (Laurence Fishburne) explains to Neo (Keanu Reeves) that the Matrix is an illusory…
This is the eighth of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the seventh of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the sixth of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the fifth of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the fourth of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the third of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the second of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
This is the first of an eight blog post series where I’ll attempt to make a version of each of the Common Core State Standards’ Math Practices that educators, parents, and students can all understand. Simply put, the Math Practices are really tough to make sense of, which means that few educators have read them…
Here’s a question to think about: if you can completely remove a problem’s context and still solve it, can it really be mathematical modeling?
Consider the math problem below from a middle school math textbook. It uses the context of a baseball diamond to discuss rational numbers. It is listed as a “Real-World Link” and demonstrating Math Practice 4 (notice the box in the upper right).
I was watching students work on this page and wondered how important the context was to solving these problems. Then it made me wonder, “What if there was no context? What would change?” This is what the problem might look like it the context was completely removed.
I recently attended a full day workshop with Jo Boaler where she shared a different way of thinking about convincing someone from Thinking Mathematically by J. Mason, L. Burton, and K. Stacey. In the book, she identified three levels of convincing: Convince yourself Convince a friend Convince a skeptic I immediately realized that this…
When teachers begin to implement problem-based learning, several questions consistently come up and I have a slide to discuss them during my presentations. At the 2014 California Math Council (CMC) North conference in Asilomar, Michael Fenton mentioned that these questions would be worth sharing in a blog post. Anyone else think @robertkaplinsky should write a…
I wanted to share a resource from Tina Cheuk out of the Understanding Language department at Stanford University who created a very useful graphic organizer to show that the Common Core State Standards (CCSS) for Mathematics, English Language Arts (ELA), and Next Generation Science Standards (NGSS) have significant overlap and can be collectively implemented for…
How do the Common Core State Standards‘ (CCSS) description for how students are expected to demonstrate their mathematical understanding compare to the Texas Essential Knowledge and Skills‘ (TEKS) description? I wondered about that question as this summer I will be doing my first workshops and presentations in Texas. As I primarily work in California where…
How do you think 32 eighth grade students would respond to this nonsensical question: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”* Take a guess as to what percentage of them would give a numerical answer and then watch the video below: Of the 32 students I…
Below are links to PDF copies of the Common Core State Standards’ Standards for Mathematical Practice in multiple languages. Please let me know if you have them in any other languages so I can add them to this list. Armenian Chinese Korean Spanish Tagalog
Math content and language objectives can be challenging to create, especially when you don’t want to explicitly tell students what they will be learning at the beginning. Additionally, if your school is using the Sheltered Instruction Observation Protocol (SIOP) model, content and language objectives are required for every lesson. Fortunately, the Common Core State Standards’…
Have you looked at a mathematics problem-based lesson and thought that while it would be fun to do one with your classes, you weren’t sure if it would work with your students? Maybe you’ve already tried out a few lessons but keep running into the same issues? This Tuesday at 9 PM EST I will…
Several years ago I had a profound moment that led me to completely rethink what it meant to understand mathematics. I was still in the classroom and had been working with 6th graders on adding and subtracting mixed numbers. My formative assessments and observations showed that most students were proficient, and I felt pleased. To…
Many teachers reading the Standards for Mathematical Practice are confused by what “Model with Mathematics” (Math Practice 4) means. I define mathematical modeling as the process of taking an often real-world context, turning it into something you can manipulate with mathematics, and then returning to the context with the new knowledge. For example if you want…