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The Reflective Educator

Formative Assessment Responses

Formative assessment means more than just giving a quiz or an exit ticket. An assessment is only formative if the teacher (or her students) respond to the information gathered.

However coming up with an appropriate response is typically hard to do. After all, the most common finding in formative assessment is that a significant, but perhaps minority, group of students still do not understand a concept, after the teacher gave her best shot at helping students understand. No teachers save their best strategy for teaching a topic until later.

Two different approaches to teaching

Here's an approach to teaching about the relationships between the different forms of the equation of a line that is based on constructivism.

Magdalene Lampert on Ambitious Math Teaching

This is a video of Magdalene Lampert taking about Ambitious Math Teaching. I'm sharing it mostly so I don't forget where it is.

This Kind of Teaching

I read an important passage in Elizabeth Green's book "How to Build a Better Teacher" and decided that I had missed something important when reading about Magdalene Lampert's teaching. Below is a summary of some of the important features of her teaching as I see them. The first tweet is the thing that I had misinterpreted as students talking to justify their reasoning, which is similar but not exactly the same as students talking to prove their reasoning is correct.

A catalog of mathematics education resources

I'm tired of having to search all over the place to find the-link-to-that-mathematics-resource-I-really-want-now-and-bookmarked-a-year-ago and so I created a spreadsheet to keep track of the various mathematics resources as I learn about them. Yes, I know I could have done this with Diigo or Delicious, but I prefer the portability and simplicity of a spreadsheet.

Grand Challenge for NCTM

NCTM recently asked for Grand Challenges that are ambitious but feasible, positively impacting many people, and which should capture the public interest. Here is my grand challenge:

  • Develop a comprehensive, national professional development model that supports the high quality mathematics instruction they have been promoting for many years.

 

Here's what I think that could look like:

Why is it so hard to change math education?

Imagine you are asked to learn about something, and the only way someone can help you understand it is with words, because there are too few examples of it around to actually see it for yourself. You think you know what it is they are talking about, but you keep getting confused because your image of what it is seems so much different than what the other person is describing.

Categorizing Student Strategies

For the last two years, the project I am currently working with has been asking teachers in many different schools to use common initial and final assessment tasks. The tasks themselves have been drawn from the library of MARS tasks available through the Math Shell project, as well as other very similar tasks curated by the Silicon Valley Math Initiative.

The Confirmation Bias Cycle

Educational research flow-chart

 

I've been working hard to read research carefully, both research with which I agree, and research with which I disagree. I still struggle with my tendency to overlook the flaws in research with which I agree, and to find fatal flaws in research with which I disagree.

Ineffective feedback and the Khan Academy

According to Grant Wiggins, there are seven essential elements of effective feedback.

Feedback should be:

  • goal-referenced,
  • tangible and transparent,
  • actionable,
  • user-friendly,
  • timely,
  • ongoing,
  • consistent.

 

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