tag:blogger.com,1999:blog-43089642985768004922017-07-23T03:16:55.152-07:00Coach K's Math BlogBlog about Mathematics and Teachingrichkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-4308964298576800492.post-62217074217400666532013-05-28T19:55:00.004-07:002013-05-28T19:57:38.607-07:00Stop the Craziness!I love mathematics and teaching. I believe all students have greatness in them and can learn mathematics at a high level. Without a strong math foundation, over 50% of my students dreams cannot be fulfilled. I teach my students to dream big and be great, not good, but great at what they do in life. <br /><br />It's been a week since I saw the new SBAC math pilot test for high school. Since, then I wake up at night thinking that parabolas and exponential equations are chasing me. I dream of $$$, on how much SBAC is going to charge my district for student's to practice on the computer, buy materials, and pay for the improvement plans. Also, I've applied to get a master's degree in mathematics, so I don't have to go through the embarrassment of being a high school math teacher once the results of this testing comes out. <br /><br />What I saw was a complete disconnect between the standards and how to properly assess mathematics. The standards are supposed to be deep understanding, not "a mile wide and inch deep", but the pilot questions were exactly "a mile wide and inch deep".<br /><br />There were two major flaws in the pilot test: (1) The questions themselves and (2) the use of technology. I wrote a blog about the technological problems here: <a href="http://coachkmath.blogspot.com/2013/05/sbac-follow-up.html">SBAC Follow Up</a>. The question themselves were written for students with a high reading and high math level. This screws students who are good in math but struggle with reading (me). At least on the ACT or SAT, you have a chance at a decent score in math if you do not read at the highest level. So its a double edge sword for math teachers and students, not only do you have to know about mathematics but they also need to be very good readers. I understand that we need to raise the bar, but setting it beyond the capabilities of our young is very troubling.<br /><br /><br />Other random observations:<br /><ul><li>The pilot high school test we took did not include trig, logs, complex numbers, and many geometrical standards.</li><li>No offense to the writers but I found a sick love of completing the square, parabolas, throwing balls, difficult factoring, multiplying many many terms, geometric proofs, and simplifying unnecessary fractions. </li><li>The difficulty level was extremely high, out of 60 to 74 questions, I'd say there were less than 5 questions that were straight forward and did not have multiple parts.</li><li>There is no way any student could legitimately get through the test in two hours.</li><li>The calculator was only allowed on certain problems.</li><li>After 15 questions, it saved the work and students could not go back to those questions.</li><li>Unclear directions: Should students simplify completely? Write the abbreviation for units?</li><li>Questions ran off the screen, which drove students nuts. </li></ul><div>Here's an example of type question that may have been on the pilot exam.<br /><br />Solve:<br /><a href="http://1.bp.blogspot.com/-wmarM2eEwdk/UZ1zRVJChgI/AAAAAAAAAAQ/rOf_oAgZdYY/s1600/Eqn2.gif" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-wmarM2eEwdk/UZ1zRVJChgI/AAAAAAAAAAQ/rOf_oAgZdYY/s1600/Eqn2.gif" /></a><br /><br />There's nothing wrong with this problem, except it's way too complex for most students. I believe this is an example of an "easy" problem. Thanks to SBG (Standards Based Grading) see <a href="http://shawncornally.com/wordpress/?page_id=114" target="_blank">Shawn Cornally's</a> blog for further information about SBG, I know that this is an extremely difficult problem for students.<br /><br />Here's the breakdown:<br /><br />for (x + 3)^2 = 16: 77% of students get this correct. N = 92 (sample size)<br />for 2(x +3)^2 = 32: 51% of students get this correct. 37% get both solutions<br />for 2(x+3)^2 + 7 = 39: 36% of student get this correct. 22% get both solutions.<br /><br />The scoring for this would be interesting. Do they get full credit for one of the two solutions? What if they left the answer in radical form or x = –3 +/- 4? What if they write x = 1 AND x = –7 instead of x = 1 OR x = –7, or x = 1, –7? How does the computer score this? I'm sure we'll never know how they scored this problem (unless we pay for it).<br /><br />I believe if you want to know if students can solve from the vertex form a quadratic the problem (x + 3)^2 = 16 would be a better choice. Perhaps, a better way to assess solving a quadratic function would be a problem like x^2 + 10 = 19, where they could factor it or isolate x.<br /><br />Another issue was the complexity of the multiple responses. A student should not have to multiply a binomial times a trinomial, five times to demonstrate they understand equivalency. That problem took students 5 to 10 minutes, if they tried it at all.<br /><br /></div><br />As my students struggled to answer questions, a cloud of frustration hovered over the room, then atmosphere moved to a near riot. My best students worked through problems at a blistering rate of 20 per hour (there were between 60 and 74 questions). So in two hours, they might get 40 to 50 done. At least some of my students were able to swiftly figure out how to move to the next question and "get through" all 74. :)<br /><br />I know students rushing through the test may improve as students take test after test, year after year, but I have a feeling what I saw will be the norm. Some will try, others will try and finish as fast as possible. I know they do this now on the Michigan Merit Exam, but until I saw them take the test on computer without bubbling, it never really stuck in my brain, that I can't make students do their best on these tests. And this one of my best classes I've had in my career, I'd hate to think what some of the bad ones would do.<br /><br />What scares me the most is that I've done this type of mathematics (talking about the Common Core and SBAC testing) before, it was called the Core Plus Mathematics Project. For seven years, I taught Core Plus. It took four years just to understand it, then three more to get students to an average level, then my district pulled the plug because students were doing horrible in college math classes and on the ACT. The intent of Core Plus was good, but it ultimately failed because it required to deep of understanding of math and too high of a reading level.<br /><br />As a teacher I take great pride in learning and honing my skills, through blogs, other math teachers, workshops, and conferences. I stay up-to-date on technology and what skills my students will need to be successful in math. From <a href="http://blog.mrmeyer.com/" target="_blank">Dan Meyer</a> to Wayne State University's Dr. Steven Kahn's award winning <a href="http://www.mathcorps.org/Default.asp?bhcp=1" target="_blank">MathCorps</a>, there are many exciting ways to learn mathematics, unfortunately the SBAC pilot test contradicts everything the math world is doing to improve math education. <br /><br />Overall, this experience was gut-wrenching, frustrating, and a huge let down. I wish my students did not have to waste their day taking it, nor see that everything they learned about math in the last ten years is obsolete. I think a lot of us would love to have a real crystal ball or see the future like Jedi Knights, for one day I got see the future and I wish not to see it again. <br /><br />richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0tag:blogger.com,1999:blog-4308964298576800492.post-10075003584101805462013-05-28T17:46:00.000-07:002013-05-28T17:46:26.821-07:00SBAC Part 2 - The Questions.Random observations:<br /><ul><li>The pilot high school test we took did not include trig, logs, complex numbers, and many geometrical standards.</li><li>No offense to the writers but I found a sick love of completing the square, parabolas, throwing balls, difficult factoring, multiplying many many terms, geometric proofs, and simplifying unnecessary fractions. </li><li>The difficulty level was extremely high, out of 60 to 74 questions, I'd say there were less than 5 questions that were straight forward and did not have multiple parts.</li><li>There is no way any student could legitimately get through the test in two hours.</li><li>The calculator was only allowed on certain problems.</li><li>After 15 questions, it saved the work and students could not go back to those questions.</li><li>Unclear directions: Should students simplify completely? Write the abbreviation for units?</li><li>Questions ran off the screen, which drove students nuts. </li></ul><div>Let's look at one of the problems from the teaser.<br /><br />Solve:<br /><a href="http://1.bp.blogspot.com/-wmarM2eEwdk/UZ1zRVJChgI/AAAAAAAAAAQ/rOf_oAgZdYY/s1600/Eqn2.gif" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-wmarM2eEwdk/UZ1zRVJChgI/AAAAAAAAAAQ/rOf_oAgZdYY/s1600/Eqn2.gif" /></a><br /><br />There's nothing wrong with this problem, except it's way too complex for most students. I believe this is an example of an "easy" problem. Thanks to SBG (Standards Based Grading), I know that this is an extremely difficult problem for students.<br /><br />Here's the breakdown: for (x + 3)^2 = 16: 84% of students get this correct.<br /> for 2(x +3)^2 = 32: 51% of students get this correct. 37% get both solutions<br /> for 2(x+3)^2 + 7 = 39: 36% of student get this correct. 22% get both solutions.<br /><br />The scoring for this would be interesting. Do they get full credit for one of the two solutions? What if they left the answer in radical form or x = –3 +/- 4? What if they write x = 1 AND x = –7 instead of x = 1 OR x = –7, or x =1, –7? I'm sure we'll never know how they scored this problem (unless we pay for it).<br /><br />I believe if you want to know if students can solve from the vertex form a quadratic the problem (x + 3)^2 = 16 would be a better choice. Perhaps, a better way to assess solving quadratics would be a problem like x^2 + 10 = 19, where they could factor it or isolate x.<br /><br /><br /><br /><br /><br /><br /><br /><br /><div><br /></div><div><br /></div><div><br /></div></div>richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0tag:blogger.com,1999:blog-4308964298576800492.post-75834110293133409352013-05-24T21:00:00.002-07:002013-05-24T21:00:53.926-07:00Main Principle of Addition"You can only add the same things, when you add the same things, you get the same things."<br /><br />This works for preschoolers to Calculus students. Stop the craziness, adding doesn't change as students get older. I've had several discussions with my students trying to convince them that 2(3)^2+4(3)^2 = 6(3)^2 or 2|x+3| + 4|x+3| = 6|x+3| is the same thing as 2 apples + 4 apples = 6 apples. <br /><br />We spent a lot of time teaching what the "Things" are. <br /><br />This works awesome with fractions, the denominator is the thing that is the same thing. By teaching the main principle of addition, students actually don't skip fraction problems!<br /><br />Btw, subtraction is just adding the opposite.richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0tag:blogger.com,1999:blog-4308964298576800492.post-51802298629686094442013-05-23T08:55:00.001-07:002013-05-23T14:08:30.303-07:00SBAC: Part 2 TeaserHere we go.<br /><br />Solve:<br /><br /><div><a href="http://1.bp.blogspot.com/-wmarM2eEwdk/UZ1zRVJChgI/AAAAAAAAAAQ/rOf_oAgZdYY/s1600/Eqn2.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-wmarM2eEwdk/UZ1zRVJChgI/AAAAAAAAAAQ/rOf_oAgZdYY/s1600/Eqn2.gif" /></a></div><div><br /></div><div><br /></div><div><br /></div><div>Simplify:<br /><br /><a href="http://3.bp.blogspot.com/-zf4PQroyhTc/UZ10J7oeXsI/AAAAAAAAAAg/YhVsg5fNbSI/s1600/Eqn3.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-zf4PQroyhTc/UZ10J7oeXsI/AAAAAAAAAAg/YhVsg5fNbSI/s1600/Eqn3.gif" /></a></div><div><br /></div><div><br /></div><div>Find the average rate of change when the function is increasing.<br /><br /><a href="http://3.bp.blogspot.com/-34OgqJepnms/UZ12JtnEOZI/AAAAAAAAAAw/TUGAWwAQnMw/s1600/Eqn4.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-34OgqJepnms/UZ12JtnEOZI/AAAAAAAAAAw/TUGAWwAQnMw/s1600/Eqn4.gif" /></a><br /><br /><br />Find the mean grade in each class. (You cannot use a calculator)<br /><br />Class 1: 77, 78, 83, 84, 98, 99, 66, 76, 78, 99, 94, 94, 95, 92, 89, 75, 72, 85<br /><br />Class 2: 66, 75, 88, 96, 98, 77, 78, 88, 35, 92, 88, 84, 67, 68, 88, 93, 84, 56<br /><br /><br /><br />These could be something similar to the least complex problems.</div>richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0tag:blogger.com,1999:blog-4308964298576800492.post-60390409214873684272013-05-22T17:24:00.003-07:002013-05-22T17:36:35.317-07:00SBAC Follow UpThanks for the overwhelming responses. This subject fascinates me and it seems like it struck a nerve with a lot of people. I'm going to attempt to divided this into 3 parts: (1) Testing on computers, (2) The test itself, and (3) student/teacher responses.<br /><br />Intuition is sometimes good and sometimes bad. I had a feeling students would treat the SBAC test like the Khan Academy. My thoughts were confirmed as my students worked through the test. Many asked why they couldn't "see if they were correct" like other tests they've taken on a computer. Most spent 2 minutes on a problem, even though the problem should have taken 5 minutes, and moved on. After about 10 minutes, students started clicking answers so they could move on to the next question (which is the only way to move on), to find "easier" questions. I was surprised to see that their attention span and determination was significantly less on a computer than a paper and pencil test.<br /><br />Another interesting thing, is how difficult is was to monitor students. The computers are lined-up next to each with only maybe a foot between them in two rows. I was surprised how easy it was for a student to look at someone else's computer screen. I'm not sure if I was supposed to help students with the graphing tool or equation editor, but I did anyway. This is where SBAC will make some serious money, because students will have to be proficient using the equation editor, graphing tool, calculator, and regression tools before they take the test or the will lose valuable time trying to figure it out. The practice test will, of course, cost $$$. <br /><br />An example of the problem with the equation editor is that it is not intuitive. Students had to write a polynomial say 9x^2 + 5x + 1, they entered the "9" then pressed the box for exponents, the "9" turned blue, they after many tries, we figured out that we had to right arrow so the "9" was black instead of blue, then type the rest of the equation. I wonder if full credit would be given for 9x^2 + 5x + 1 instead of the equation editor look.<br /><br />This leads me to my last part tonight about using computers. There were many instances like the last example where an answer could be given in different forms. How is this scored? Are computers capable of distinguishing between "root 45" and "3 times root 5" as acceptable answers? What if a student wrote in words instead of numbers? Again, this will be a money maker because it will force districts to buy the practice materials.<br /><br />There are more technological issues, but my brain needs some rest.<br /><br />Remember this: We are all in the same boat, we can chose to sink or find a way to make it float.richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0tag:blogger.com,1999:blog-4308964298576800492.post-42168325321713153572013-05-22T06:43:00.001-07:002013-05-22T06:49:08.005-07:00SBAC Pilot Test for MathI had the privilege of piloting the SBAC Pilot Test for Math yesterday. We have a new four-letter word that should be grouped with words we shouldn't say. Since I had to help most students on almost every problem, I got an in-depth look at the SBAC testing. <br /><br />So here's the good, the bad and the ugly.<br /><br />The good...<br /><br />The bad...Students treated it like most computer programs, they click and click and filled in answers quickly to move to the next question. It was like watching them on the Khan Academy, but not getting feedback on whether they were right or wrong, and no gold stars.<br /><br />The ugly...The first student revolt began 11 minutes and 45 seconds into the test when they couldn't figure out the line graphing tool. The second revolution came when students had to use an awful equation editor to write a quadratic equation. The third and final revolution came when we couldn't decide which correct answer to chose since there were two correct answers. This was just a few example of the many "technology" issues.<br /><br />The really ugly...The test itself was harder than any college entrance math exam or teacher certification test. It was poorly written and focused on the same couple of things over and over and over again. It was the high school test, yet there was no trigonometry, logarithmic functions, complex numbers, nor any of the Common Core "Algebra 2" questions. <br /><br />Overall, it sucked. My students hated it. The look on their faces told me that we are in trouble once 50% of our evaluations depend on it.<br /><br />More to come.richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com2tag:blogger.com,1999:blog-4308964298576800492.post-92192204216623740492012-05-25T18:35:00.000-07:002013-05-22T17:37:47.880-07:00What is Algebra?<br /><br />A couple of years ago this question was asked at a conference, by Dr. Kahn from Wayne State University. We knew what Biology, Psychology, and Geography we but could not define Algebra.<br /><br />How could 35 math teachers not define something we are so familiar with?<br /><br />The answer is so simple, yet I think it underlines a serious problem with math education in that we make things too difficult.<br /><br />Dr. Kahn gave us an example of how hard English is to learn. The word "laugh" should be "laf" and how can "air" be spelt as in "bear", "care", "their", "they're", and "fair". The reason for this is that English is a mix of languages and there was no one person "in charge" of how it should be put together. <br /><br />Math didn't have anyone in charge when things were invented and it has the same complexity as English but it is acceptable to not learn math. You'd never hear someone saying "I wasn't good in English, its ok not to learn it". Math gets beaten down, even by our own teachers.<br /><br />How do we fix this? We need to make math simpler, not easier, but simpler. I believe that Dr. Kahn has the first piece (and many others) to the puzzle. Algebra is the "study of operations". Think about it, "the study of operations". Biology is the "study of living organisms", now Algebra is the "study of operations".<br /><br />How cool is this? This blew me away. How can all of the 500+ standards and benchmarks in high school math boil down to adding, subtracting, multiplying, and dividing; and if you really put some thought into it, Algebra is about adding and multiplying.<br /><br />It's amazing to see students brains light up after I give them the answer to the question "What is Algebra". It makes sense and it gives my class a clear focus throughout the year.<br /><br />The "Study of Operations" is the first step in the quest for getting all of our students through Calculus in high school.<br /><br />Homework: Ask you colleagues this question at your next meeting, see how many of them can define Algebra.<br /><br />*By the way, I've asked this question to about 500 students and still haven't had one come close to being correct.<br /><br /><br /><br /><br />richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0tag:blogger.com,1999:blog-4308964298576800492.post-87367296111697315572012-05-22T16:49:00.003-07:002012-05-22T17:15:59.153-07:00WelcomeHello to all visitors, I hope this blog can inspire you about teaching and learning mathematics. My mission is to get every student and teacher literate in mathematics.richkonarhttp://www.blogger.com/profile/03385456705091200695noreply@blogger.com0