Greenhaus Education and Other "Effects"

Wow - can't believe I haven't posted since May.  Crazy.  Of course, I do post weekly on my other blog, so I am going to plead busy!! It has been busy these last few months.  I have been doing some very diverse things, all related to math education. It's one of the benefits of going out on my own and being "independent" - I get to try new things and do a variety of math and technology related activities which keeps me interested and on my toes.  Here's just a few things I have been doing since May: 1) Working for Casio - so blogging, Tweeting , Facebooking and doing research on technology, BYOD, testing etc. 2) Working for the Dana Center at UT, Texas and DoDEA (Department of Defense Education Activities) as an International Fellow supporting their adoption of College and Career Ready Standards. I went to Austin, Tx for some training and just got back from England, doing training at LakenHeath Air Force Base.  Such a marvelous experience! Heading to...

My daughter sent me this article, Parents are Freaking Out Because They Can't Answer a 7-year Olds Exam Question,  the other day concerning a Twitter posting about a math problem that was frustrating students, parents, and lots of people on Twitter obviously. Here's the problem: The issue is there are two answers that could be correct: 65, if you use the 'work backwards' method, subtracting out the 17 that just got on from the 63 and then adding back the 19 that got off.  The other answer is 46, which results from simply subtracting out the 17 that just got on from the 63 currently on the train.  The teachers exam rubric/'test key" stated the correct answer as 46.  Hence - all the confusion, because that would mean the 19 was an unneeded number. The real problem here, and it is NOT an isolated situation, is that this question is very poorly worded, and thus open to both interpretations. The work-backwards approach assumes that the question is asking ...

I have read a couple articles of late that have kind of pissed me off.  Mainly because they perpetuate the ideas that 1) The Common Core State Standards are handed down from the Federal Government, and 2) that the CCSS are the driving force behind Standardized Testing.  While there are connections, both claims are a complete disservice to the purpose behind and the reason for The Common Core State Standards. And they completely ignore the fact that Standardized Testing is actually controlled by testing companies and publishing companies. I've already posted on this before - " What People Think Is Common Core ISN'T"  and "Common Core, It's NOT the Devil"   so I apologize now for being repetitive. One article I read last night, entitled " What's the largest number you can represent with 3 digits? Nope. It's not 999."   is a great article. I agree with everything the author said and applaud his sticking by his daughter, the second teache...

I read this article the other day by Dana Goldstein , "Down with Algebra II!" , which describes professor Andrew Hackers views on mathematics, and how the push for STEM, higher math like Algebra II, is actually creating a the failure and dropout rates we are seeing because it is pushing students into mathematics that is not necessary for their future endeavors and "destroying a tremendous amount of talent". The math requirements in high school and college are "highly irrational". And then my friend sent me the same exact article via Facebook and asked my opinion. (This is what happens when your friends know you are a math person!). So - what is my opinion? I have to say, I completely agree with Andrew Hacker. In fact - I have written about it before a few times: Math Curriculum - What should we be teaching?;  Financial Literacy - Real-world math, REALLY ; Let's teach probability & Statistics - We need it!   Don't get me wrong - I think Al...

NCTM is coming up in April and is in San Francisco, which has me very excited because I get to have a Key Curriculum reunion (i.e. my colleagues from my years working for Key Curriculum mostly live in the SF area).  It's hard to describe the amazing connection those of us who worked with Key, (Keysters, as we fondly refer to ourselves) have, and I have yet to find another place or another group of people that I so deeply connect to on both a professional and personal level. With this math conference and potential to see so many of my former colleagues, I have been a bit nostalgic about some of the things I loved from Key - i.e. Sketchpad and TinkerPlots to name a couple.  Sketchpad , now owned by McGraw-Hill, is still around thank goodness, but without the support and push in math education it deserves.  Thankfully, some former Key folks are still out there making a difference with Sketchpad - check out Daniel Scher and Scott Steketee's most recent article in The M...

There are a lot of Open Educational Resources out there, which is exciting if you are a teacher, as you can find myriad of lessons and ideas.  The big issue with OER is of course the quality of what you find, does it really align to your instructional goals, and naturally, do you have the time to search through possibly hundreds of resources to find that perfect fit. In my recent work, I have been exploring The OER Commons website, which is a digital library and network of Open Educational Resources. It allows you to search, with a search feature that really lets you refine down to exactly what you are looking for - whether that be full lesson plans, videos, full units of study, online courses, etc. You can also review and comment on resources, which is a nice feedback feature that allows for others to gain from those who have used a resource. You can create your own content to share or link to others and collaborate. Fig 1 What I particularly like, as a certified Common C...

Yes, there is some thinking-differently going on, at least in Florida. There is a bill in the Florida House of Representatives to make in-person and virtual computer-science classes count as Foreign Language credits towards graduation.  THAT. IS. AWESOME! I am all for changing the way we teach and what we teach and where we teach in this country. I would love for us to break out of our traditional classrooms of desks in rows and teachers as sages, and let students have more choice in subjects they, and have more options of courses.  For example, not every student needs calculus, but EVERYONE needs Personal Finance - and yet, it is not an option in most school districts, or if it is, it is often an add on. (See my previous posts on Financial Literacy if interested....1)  Math Curriculum - What Should We Be Teaching 2)  Financial Literacy - Bring It Back to School!  and  3) Financial Literacy -  Real-World Math, Really! ) Math itself is a f...

I was listening to NPR this morning, as usual, during my workout. The Pulse did their entire hour on the Rebirth of the Library .   As an avid reader, this was of great interest to me. I love books. I have a crazy collection of books, all down in my basement now since I live in a tiny house with little room for my shelves and shelves of books. But - I don't have the heart to get rid of them, and I do reread them - it's like coming home to old friends.In fact, I just reread over the holidays The Lord of the Rings Trilogy (an annual tradition)...which can only be done correctly with a the actual book that allows me to flip back to the maps a million times. NPR's many stories related to the library included many things about how libraries of today are still relevant, and how many libraries are changing. I would suggest reading/listening to the different stories. The one that really sparked my mathematical interest however was the one by Peter Crimmins entitled Will BookBo...

"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 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 ...

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 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...