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Posts Tagged ‘NC common core’

The problems with Common Core Math 2 – why students are failing

18 Jan

As I watched one of the students I tutor fail Common Core Math 2 for the semester, I can’t help but ask myself, what did I do wrong?  Another student, passed the class (with an A, I believe) but failed the exam (the teacher chose not to count the exam towards the course grade).  Any quality teacher who has students “fail,” should ALWAYS ask themselves, “What changes do I need to make?”

So, I pondered this question.  I looked at the type of student that each student was, the type of teacher each student had, the school each student attended, and the work we did together in our tutoring sessions.  I was able to find my answer after these considerations.

The first piece of the puzzle comes from the type of student I worked with.  One student was a student who spent many hours studying and lots of extra effort above and beyond our tutoring sessions.  I also like to rank each student with how “easy” math comes to them.  On a scale from 1 to 10, with a 1 representing a student who really struggles to grasp mathematical concepts, struggles with number sense, and just doesn’t have a logic / math brain to a 10 where the student just “gets” math without even trying, math just makes sense automatically and is like breathing, I will rank each student to provide prospective.  This student is probably around a  7.  The other student did not spend any time outside of our tutoring sessions working on math, didn’t really see doing well in math as a priority and ranks lower around a 5.  She doesn’t get totally lost but can’t seem to put the ideas together and connect them.  She also doesn’t spend time memorizing what is needed to do well.

The second piece of the puzzle comes from the school system, school and teachers these students have.  Both students are in the same school system but at different schools.  One school clearly has higher expectations than the other school and tends to ask harder questions on tests.  Neither teacher seemed “terrible” or “good.”  Neither teacher seemed to care too much about the success of their students based on my interactions / discussions with their families.

These previous two pieces certainly play a role in student success.  From me, both students got the same help from me but students need to spend outside time studying, memorizing, and practicing problems to be successful.  However, one of the biggest challenges I see is that the pace of the curriculum, especially since this school system uses block scheduling (math classes are 90 minutes a day and an entire math class is completed in 1/2 year).  If you have a student who ranks a 7 or above, they can probably handle the pace of learning Common Core 2 in one semester but for students who struggle with math (especially for those with weak math backgrounds, poor number sense, poor study habits, etc.) expecting them to be able to pass Common Core Math 2 in one semester is akin to expecting someone to become an expert on Calculus in 10 days of lessons.  There is only so fast someone can learn information and that is not being taken into consideration.  Why aren’t we offering a Common Core Math 2A and 2B class for students who need to learn at a slower pace?  They did this for Common Core Math 1 (in fact that is your only option in our county) but for Common Core Math 2, your only option is to learn the entire content in 1 semester.  For bright / math minded students, it is a good option and should remain so that these students can move ahead and take AP Calculus and AP Statistics during high school but for the average or below average student (in mathematics), we need to offer math at a slower pace.

Currently, we pass students on with a D in Common Core 1 into this fast paced Common Core 2 class.  Students with a D in Common Core 1, are not prepared to even take the content of Common Core math 2, let alone take it at the pace of 1 semester.  Many of these D students were “gifted” their D’s as I have witnessed.  I have students who can’t solve a basic linear equation on their own, couldn’t tell you the difference between linear, quadratic, and exponential equations, and couldn’t solve or graph any quadratics receive a D in the course and now I know they will be completely lost and unsuccessful in Common Core 2 because they do not have any of the prerequisite knowledge needed for success in Common Core 2.  Yet, teachers continue to “pass” students along because they can’t “fail” too many students or they will get in trouble with the administration.

We seem to forget what the goal is.  Do we want to just pass students along or do we want them to have an understanding of mathematics that makes them college ready?  If we need to slow things down, allow students more time, allow students to repeat classes, then this is what we should do.  We also continue to allow lateral entry teachers because we are short on math teachers, yet we don’t value them.  Lateral entry teachers (and many current teachers) seem to lack the skills needed to help students learn how to study mathematics, another important step for success.  Rarely do I see students come to me with a list of topics they will be covering, review sheets with problems and solutions that are representative of what they will be tested on for quizzes, tests, and finals.  If students had these materials, they could learn more effective ways to prepare for mathematics assessments and be more successful instead most of my students have no idea what to expect on their assessments and no problems that are representative of what they are supposed to know and practice right before an exam.

 
 

Alternative Ways to Teach Mathematics for Common Core – in response to video for TERC

03 Aug

What do you think about this?  This came from a site called Stopcommoncorenc.org

 

Note this link comes from a site that clearly has a negative opinion about these alternative methods.  Is she justified?  Well, let’s not jump to conclusions and say, “Yes.”  I think the answer is “almost yes.”  I am a firm believer that nothing is ever black and white.  Common Core mathematics encourages students to learn alternative ways of thinking about mathematics.  They encourage students to delve deeper into the meaning behind the computation.  They want students to know the meaning behind an algorithm at a mature level.  This is a very LOFTY goal.  In fact, after doing my dissertation, I learned that many teachers don’t even have this level of understanding.  My daughter was taking 5th grade mathematics this past year using the North Carolina Common Core curriculum.  She was required to solve all her problems three different ways and then she had to write a journal entry that explained the WHY behind what she did.  This really isn’t too far off from what is in these videos.  Of course she was also taught or allowed to use the standard algorithm, but only in addition to other less effective algorithms that she had to learn.  These less effective algorithms were meant to build her conceptual understanding.  Was it effective?  I really don’t think so.  I don’t think you need alternative algorithms to build conceptual knowledge.  I think you can just build conceptual knowledge with good teaching.

For example, I have no idea how TERC might teach adding mixed numbers but when I look at how to teach this I know that some teachers (most) would teach it by just teaching the algorithm:

2 3/4 + 1 3/4

1.  Add 3/4 + 3/4  = 6/4

2.  Convert 6/4 to    1    2/4

3.  Add the whole number pieces:  2 + 1 + the extra 1 from step 2 = 3

4.  Final answer 3    2/4  or reduce to 3  1/2

 

However, a better approach might be to demonstrate this with a concrete approach rather than starting abstractly with just numbers.

Draw 2 and 3/4 a pies and another 1 3/4 pies.  Show how you can move one piece of the second partial pie to fill up the other partial pie, giving you 3 full pies and  2/4 left over pie (or 1/2 left over pie) – final answer 3 2/4 or 3 1/2.

From here you can now relate the concrete picture to the abstract numbers.

 

This is what I mean by “good teaching” and is much better than using 3-4 additional ineffective algorithms or “discovery” learning approaches.  Discovery learning was something that I was introduced to in my methods class when getting my degree to become a teacher.  It seemed like such a good idea at the time, instead of you telling the student what the answer was or how the problem worked, you devised a lab situation where they naturally “discovered” the solution all on their own.  Since they created it, it was more active learning and hence would stay with them longer than just being told.  The idea sounds great and active learning DOES produce better retention.  The problem is that you have to actually create that situation you are looking for.  If you just give them labs that the teacher THINKS will lead them to building conceptual knowledge but instead just ends up being a lot of extra steps (see the first video example), the impact is the exact opposite.  Our local high school tried this.  They decided to teach Common Core Math 1 concepts through discovery learning.  Instead of giving lectures on exponential functions and showing relationships, demonstrating examples, and having students work problems, they created these lab experiences for these freshmen (and a few sophomores) to do.  The students that I worked with completed the labs but it was clear that they had no meaning for them.  The intent was that this was supposed to build all the concepts they needed about exponential functions when in fact, the students just found answers to questions without piecing together the big picture or linking one lab to the next.  It was an utter failure.  Discovery learning is very hard to pull off.  Not only does it require really good lab experiences but it requires the right kind of student that can learn that way.   Students have a variety of learning styles and many need to be taught by concrete methods, examples, and linking new information to things they already know.

Another important point made by these videos is that it is a waste of time to teach the student the standard algorithm because they will eventually just rely on the calculator anyway.  Is this true?  Well, it is true if we make it true.  It also NEEDS to be true for some students.  If you read my post about accommodations for students with memory problems, they will NEED to have a calculator accommodation because they lack the same ability that the non-LD student has to memorize rote facts.  For this student, I think they do need a calculator so that they can focus more on the big picture and less on things that will never happen for them.  However, what about the student who can learn their multiplication facts but just doesn’t want to put in the time.  What about the 9th grader who still breaks out the calculator for 8×3?  One might argue that we always do have technology at our disposal.  With cell phones that have calculators on them, one is almost never without the ability to use a calculator these days.  Does that mean it is okay to rely on it?  I am a strong believer in technology and feel that we should not be doing tedious problems that one would not do in the “real” world without a calculator, in class without a calculator.  However, for things that one should just “know,” that demonstrates a basic understanding of basic mathematics, yes, students should be required to do these things without a calculator unless them have a documented learning disability.  In other words, let the real world determine the appropriate use of technology in the classroom.

What about the second book that was discussed in the video?  Was it all bad?  I have had students who have used both those algorithms:  the one that uses the place value and the lattice multiplication.  Here are my thoughts on those.  First, I like the idea of showing and having a lab on how 2 digit multiplication can be done with the list of numbers that show the true place value.  This really helps a student “see” what is going on behind double digit multiplication.  In fact, there are other ways that organize it even better that a teacher can use.  We do want to teach in a way that is more than just procedural mathematics.  Not all students will grasp everything but it will help some.  However, this does not mean that the ultimate goal is to leave out the standard algorithm.  The other algorithm is used to demonstrate conceptual understanding, not to be an algorithm that students continue to use.  My student who did try to use this as their only algorithm, did make many more mistakes than students using the traditional algorithm.  As for the lattice method, there is no reason conceptually to show this method.  However, for some students, the organization (keeping things in boxes) helps them from a visual perspective and that is why a teacher might choose to show this.  The student that used this algorithm used it successfully for a long time, he is a rising 9th grader and I wouldn’t be surprised if he doesn’t still use it (I only tutor him on occasion now when he has a test but it is still his algorithm of choice.)  The point of all of this is two-fold: one, use alternative approaches IF it helps a student grasp the concept more and two, allow them to use an alternative algorithm if they can be as fast, as accurate, and as effective with it.  Give the student the choice, it is frustrating when teachers tell students they “have” to use a specific algorithm.  Once a student finds one that meets the criteria of fast, accurate, and effective, they should not be forced to practice other algorithms except in sense of in class concept building labs.

Written by:  Lynne Gregorio, Ph.D. Mathematics Education