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Poor Math Questions and Misunderstandings

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 ...

Common Core is NOT the same as Standardized Testing

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...

What is the "Math Path" We Should Encourage Students to Take?

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...

Libraries, BookBots and Algorithms

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...

#HourofCode Sparking the Need for Computer Science Curriculum

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...

#Edchat Discussion - Politics, Religions & Education

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 ...

What if? A simple question to engage students.

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 ...

Back to the Future Day! Foster Creativity in Students TODAY to Build A Flying Car

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...

Common Core - #2 of Studying Structure - More on the Practices

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...

Technology for Learning - We Might Want to Ask the Students

I have been doing some independent research on technology use in classrooms.  With all the news about 1:1 classrooms and students using technology apps to learn, I was curious about what is actually happening.  Some of my findings have made me really question whether some of our approaches - i.e. 1:1, computers vs. tablets, are really supporting the way students are learning with technology. I found this interesting report from Project Tomorrow called "From Chalkboards to Tablets: The Emergence of the K-12 Digital Learner"    with some fascinating statistics regarding the technology students are using to help them learn.  You should download the full report (available as a PDF), but I will share a few of the findings here. One thing that stood out for me is the prevalence of smartphone use by students, especially as they get into the upper grades.  Table 1 below shows the use of both personal and school provided devices.  Very apparent that 1:1 and...

Dissertation Hiatus - Lesson's Learned

Well, it's been a crazy long journey, but I finally finished my dissertation and have sent it off to the committee. One more step towards this ever elusive doctorate.  Two more weeks and I defend and hopefully all these years of learning, researching, writing, and writing and writing will pay off.  I know my husband is hoping so, as he has high hopes I will get a job now!! I will say this past 11 months of 'unemployment' while I devoted myself to research, research analysis and then writing have been very interesting. I managed to start my fledgling independent consultant business and do some interesting consulting that broadened my experiences and also provided at least some financial support. I helped one company develop a webinar strategy and helped another with suggestions for PD and curriculum standards alignments. I was able to work with the technology I love, TinkerPlots and Sketchpad, and train some teachers in two different large school districts. And I did some ...

Longer School Days - Is That REALLY the Solution?

I just read yet another article about the push to lengthen the school day in order to improve student achievement entitled Learning Takes Time: Growing Movement Seeks to Expand the Length of the School Day by Celia Baker. The last paragraph of the article I think highlights the advantage of this idea: "More time and money won't help if they are not well-spent, Gabrieli cautioned. The National Center on Time & Learning report suggests that additional time be used for more engaged interaction in academic classes; broader curricula; enrichment activities that boost school engagement; and more time for teacher collaboration and professional development".  As with anything in education (think technology), if it's done right and planned out and designed to address specific needs, it will have an impact.  If it's done for the sake of being done with no real plan or purpose, it is NOT going to be effective. Adding hours to the school day so that students can ...

A Change Will Do You Good....But It Isn't Easy

I cannot believe how long it's been since I last posted. A clear sign that my life has been in a little bit of  turmoil these last few months.  But, hopefully, as the dust is settling, things will get back on a regular routine and I will not feel so completely overwhelmed. Why am I overwhelmed you ask? Change. Change in so many aspects of my life - my family, my career, my dissertation. All of it happening at once, which is probably why there is this sense of overload. Which brings me to my inspiration today. I have written about change before related to education - how teachers need support, time, etc. for change, such as Implementation Dip: It's Not Just Test Scores, It's Any Change and Instructional Change and Integration: It Takes A Village . What I wanted to focus on today is perhaps more of a justification for the time, support, understanding required of leaders as teachers (or anyone) are faced with so many challenges and changes to what, why, and how they are e...

Lecture, Direct-Instruction or Talk - There's the Confusion!

In yesterday's weekly #edchat Twitter collaboration the discussion focused on the flipped classroom, where, naturally, there was quite a bit of debate around the idea of video lectures. What became apparent was the many different interpretations of the term 'lecture'. This came to the forefront for me when I offered up the idea of TED Talks as one option for learning rather than a teacher's video lecture, and someone said "TED talks are just lectures, so how is that better?" This stumped me as I have never thought of a TED talk as a lecture, which is funny, because now, forced to think about it, I guess they could be construed as lectures, depending on your definition. Which of course has led me to this post!  Obviously, my perception of a lecture is not the same as others. What is MY definition of a lecture? Perhaps it's my many years of being both a student and a teacher, but for me a 'lecture' has rather negative connotations, as I envisio...