Greenhaus Education and Other "Effects"

"Speed ISN'T important in math. What is important is to deeply understand mathematical ideas and connections. Whether you are fast or slow isn't really relevant." - Laurent Schwartz, mathematician If you haven't seen the video by Jo Boaler and some of her Stanford students entitled "How to Learn Math: Four Key Messages", you definitely need to. Besides the four powerful messages (which I will list below), it has some great stories and quotes, one of which is the one I have above.  Jo Boaler has done powerful research and written some terrific books on mathematics and learning math (one of my favorites being "What's Math Got to Do with It?"  and the video about these four key messages in math is so interesting. Here are the four key messages about learning math (I highly recommend you watch the video to clarify and define each message a bit more): Everyone can learn math at high levels Believe in yourself (your beliefs about your ...

It's been great to see all the posts on Twitter this week and the many articles focused on National Computer Science Education Week . The #HourofCode hashtag has been lighting up Twitter this week, which has been really exciting to see (and I have loved reading and sharing all the great links). Science and teaching students coding. All of course in response to this week being The idea behind #HourofCode is to expose as many people, especially students, to the basics of coding. The hope is by showing that anyone can learn coding, need for, interest in and involvement with computer science will increase. One of the many articles I read this week was one that suggested Computer Science courses should be considered math credit .  I think this is a great idea - it would provide a valuable math credit option for students, especially those not interested in the traditional Algebra II, pre-calculus, calculus path, which is usually the push for a majority of students. Often a path comple...

I just read this article by Eric Patnoudes  entitled "Beyond the Silver Bullet: Making 1:1 Matter" .  As a parent and former teacher, Eric's basically was saying that all the technology in the world and 1:1 initiatives will fail in the classroom if teachers are not provided with the training and support they need to CHANGE their practice. Professional development needs to go beyond how to use the technology and be more about how to teach with the technology in ways that are different and more appropriate for the technology. Using the same old 20th century teaching practices with new technologies is doomed to failure. Couldn't agree more. My last post speaks to this as well - not only do we need to analyze and plan for WHAT technologies are appropriate, but we need to plan and provide continued training and support to ensure the technology purchased is being used to change teaching and support learning. In my research regarding implementing technology effectively ...

The State Educational Technology Directors Association (SETDA)  just released a paper analyzing states' policies in regards to digital materials acquisitions & implementations, along with their recommendations. You can find the report & summary here In the report, they outline Next Steps: a) Essential Conditions for successful acquisition & implementation; b) suggestions for making the procurement process transparent and easy to navigate; c) the need for strategic short & long-term budgeting; and d) and suggestions for the states to guide schools & districts on best practices for adoption, implementation and vetting of digital resources. You can read the more detailed descriptions of these four "Next Steps" recommended by SETDA here . While reading the report and the next steps suggestions, it reminded me of my own research about technology acquisition and implementation. I have done several blog posts directly related to technology implementation ...

I participated in an interesting #edchat this past Tuesday, as I try to do every Tuesday at noon (Eastern time) if it fits into my schedule.  The topic for this hour long chat was: Education should reflect culture of the country, but do politics and religion have too much influence in American education? My immediate reaction and response was yes, religion and politics have way too much influence in  American education. Two prime examples are the current hot-button issues of The Common Core Standards  and whether the word "God" should be included in the Pledge of Allegiance. Here are my personal opinions on both: "God" in schools/Pledge of Allegiance -  First of all, God was not included in the original pledge, written by Francis Bellamy in 1892. "under God" was added in 1954 in response to the Communist threat of the times But, regardless of when "under God" was added, this is just a political & religious ploy to get everyone up in ...

I am often asked by teachers how do I engage my students? What questions can I ask? Questioning is a skill that many teachers struggle with, as we are often prone to ask simple yes/no questions or one-word response questions (i.e. what's the answer?).  It takes effort and practice to ask questions that help students think, analyze their thoughts, make conjectures, etc. But, as I often tell teachers, if there a few questions that you can ask that force students away from the simple responses or the yes/no answers. Questions such as Why? of Is that always true? or, my favorite's What if? or What do you wonder? Annie Fetter, of Math Forum fame, did an incredible Ignite Talk at NCTM one year entitled "What Do You Notice or Wonder" and it really opened my eyes to the power of observation & wondering. I share it here as a here as inspiration to help you ask the questions that will invoke wonder, inquiry and thinking in students. Additionally, Randall Munroe ...

I swore to myself I wouldn't do my next post on the Common Core, but I just get so irritated by the postings I see out there about it, I can't help myself! On Facebook, I see silly things like this: And then the current huge controversy about the math quiz and the teacher grading the problems wrong: Let's not forget the multitude of articles and storylines on the news talking about parents being angry and states opting out. Thank goodness there are some people who are trying to bring reason back to this madness about the Common Core. Great response here to the quiz example above by Andy Kiersz. Or this one in response to a parents obnoxious use of what he calls "Common Core Math".  I have already written my own response to my nieces and sisters hatred of what they perceived as Common Core math in a post last year, Common Core: It's Not the Devil . The problem with all these pictures and stories and examples of problems that are "common c...

Today is October 21, 2015 and Marty McFly is set to arrive this evening, so of course, a post about the technology that actually exists today compared to what the movie predicted is in order! Someone else has done all the work for me and gone through 22 things that the movie got both right and wrong - I will let you check that out on your own. Here's a movie trailer clip that shows the some of the "things" of the future:  What I find amazing to consider is that the writers/creators of the movie were making predictions about a future 25 years down the road in a time, 1989, where none of this technology existed.   Heck - the World Wide Web was just being born in 1989. And yet now, 25 years later, some of their predictions are in fact a reality. We have 3D TVs & movies, we have Google Glasses, digital cameras, tablets, talking computers who can do things for us (Siri), and while we don't have flying cars, we do have electric cars. It's like Star Trek t...

In my final in this Common Core Structure series, I want to just spend a little time discussing the three Key Shifts of the Common Core: Focus, Coherence, and Rigor . The CC are standards - states have always had standards. The difference here is a clearer set of aligned standards, throughout K-12, that ensured the standards built on each other within a grade, between the grades, and provided a cohesive set of understandings, skills and application. Hopefully the previous four posts have given a clearer understanding of how the structure of the CC was designed to support these shifts, so now lets actually look at these three shifts in depth. I am going to use some specific standards to exemplify each shift, as I think it helps make sense of them. Focus The CC is really focused on students conceptual understanding of mathematics and their ability to apply these understandings to real-world problems. So, within each grade, there are "less" standards, and more focus to help ...

In my last post , I went in great detail into the structure of the Common Core Math Standards for K-8.  Long story short, the picture at the right is a visual of the structure showing the funnel effect – where the standard itself is the end product of so much more: Introduction, Domain, Cluster. The gist of the last post was that it is important to look at all the components, not just the specific standards themselves, so that you understand how the standard fits into the learning progression. When looking at the high school content, the structure of the standards is the same, with an additional component, the conceptual categories.  There are six conceptual categories at the high school level: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics & Probability. Within these conceptual categories, there are the Introduction, Domains, Clusters and specific standards.  The idea behind the conceptual categories is that students acquire th...

My last two posts focused on the structure of the Common Core Standards of Mathematical Practice.  The big idea of those posts was the title of the practice is NOT enough - you need to read the narrative to get to what students should be doing and saying. The theme of this post is much the same - the Common Core Math Content standard alone is NOT enough to truly understand what it is students should know and be able to do if they have mastered the content. The content standard, which is often what is posted in textbooks or put on the board, is in fact, a small part of the big picture and without seeing the big picture, we end up teaching isolated skills and facts. Understanding the structure of the content standards provides a big picture at each grade level (focusing on K-8 right now) of where students are going, and how the standards, as a whole, are continuing to develop and expand mathematical content knowledge. It is a "learning progression".I am going to focus on K-...

In the first post of my Common Core series, I discussed the importance of really looking at the Standards of Mathematical Practices (SMP), because the title alone is not enough. You cannot assume that each title of the 8 SMPs gives enough information to truly know what students should be saying and doing to enhance their mathematical understanding. The descriptive narratives for each practice are necessary reading to clearly make good instructional decisions that will truly support student understanding of mathematics My last post focused on SMP #4, Model with Mathematics. In this post, I'd like to choose another of the SMPs, and be a little more explicit in breaking down the structure to show how both the title and the narrative help inform instruction. Then, hopefully, you can do your own investigation of the remaining SMPs.  This is a great exercise to do with collaborative groups of teachers - maybe your next team/faculty meeting?! All of this is from work I have done bei...