Explain Your Answer

Shifts in Math

2000px-math-svgOne of the bigger shifts in math, aside from the building blocks in the CCSS Framework, is the ever dreaded ‘Explain your answer’. When this first came out, I wasn’t sure what they meant, the frameworks hadn’t been written yet. I had students explaining that they ‘added the ones then regrouped to get the answer.’ And while they were technically correct, there was a lot missing.

Better Understanding

Now, I have a better understanding of what is needed. The students need to break down each step and explain, using academic language, what their thought process is. I furthered my understanding when I went to a training on this. Honestly, it wasn’t the best training, but it got me thinking. I used some of the techniques to create a better lesson.

The Lesson

First, I created a template that the students were going to be using. Then, as a group, we walked through each part of the template and filled it in. There was  A LOT of guidance this first time. I’m hoping with practice, they will become more independent. Students worked in table groups to solve their table problem. Finally, they were to film their process of solving the problem. Using their ‘scripts’ students explained the process for division. Here’s an example:


So. Over. Testing.

portrayal-89189_1280Without a doubt! I have 16 days left in the school year and I need to finish 1 state test and START and complete 2 district ‘Benchmarks’. THEN if one of the district benchmarks is below a certain level I have to administer an additional assessment. Can we say, “Overkill”? If I’m feeling this way, I can’t image how over these assessments my students are.

Now add on to that the end of the year hubbub. And being 5th grade we have a few more hubbubby things to do than some other grades – tour the middle school and my personal favorite (seriously, no sarcasm here) the puberty video (boys and girls are separated). AND we are trying to finish the last 5 scenes of our movie.

I will hand it to my students, they tried super hard on all the tests thus far. Today we began the 5th-grade science test. It’s so outdated that it doesn’t align to the NGSS. And it’s on paper (we have been taking all tests online). AND, as one student so cleaverly put it, “Why did they give us all the answers?” Yeah, he was referring to the A, B, C, D choice he had.

I waited until today, only because someone asked, to break it to them that this was NOT the end of tests. It was at that point that they were officially So. Over. Testing. I felt for them. I mean 16 days. We should be wrapping things up, finding the joy in our year, ending it with fun, but instead our education system gives students a final ‘Hurrah’ with testing, testing, and more testing.

When the Common Core State Standards arrived, I was hopeful. It was to be the beginning of deep and meaningful learning and the end of high-stakes testing. I think the message got lost along the way. Fortunately, San Diego Unified SD has rethought the current testing trend. Hopefully, more school districts will follow suit.

Success In Math

Did you ever have one of those days, in teaching, where you thought, “YES! This is what it’s all about”? Yeah, I had one of those moments today.

We have been talking about place value and really digging in deep in math. Today we organically began talking about exponents. I say organically because while I’ve touched on the subject before, the students really hadn’t grasped the concept. Yet today, they began making connections. And THAT was super cool! We really only focused on exponents as they relate to the base ten number system. For example 10 x 10 = 100 = 10

This led to one student wondering if exponents “only work” with 10 or does it work with other numbers. We briefly discussed this. Then another student started making connections about the number of zeros and the exponent.

THIS is exactly what Common Core Math is about – looking deeper into the systems and the ‘why’ and discovering the connections and shortcuts. Knowledge IS power!

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3D Printer Fun

I believe in thinking BIG! That’s why when I decided I wanted a 3D printer for my class, I wrote a proposal and placed it on Donors Choose. Honestly, I had no idea what I was going to do with it. I figured I would allow students to create objects during Genius Hour. In addition, I was going to have THEM figure out the programs and printer – within reason, it is an expensive item.

So when I was notified that my project was funded by Chevron, I was beyond thrilled. Just after Spring Break our printer arrived. The following Genius Hour a group of students and I set it up. Fortunately, one of my girls had gone home and done research on the type of printer we received (Dremel). She knew more about the printer than any of us. After setting it up, we printed out a die. It was a pre-fab file on the SD Card. That was pretty cool. Then came the following week…

We discovered Tinkercad! Since then we have been creating, creating, creating! The early attempts were simple, but fun. I have students coming to school early wanting to create objects for their moms, brothers, selves…

They work together to solve design issues, and talk about new creations – there is a chicken in the making. I have another girl who went home and taught herself (with the help of the provided lessons on Tinkercad), how to use the program. She is our ‘Go To’ person. She is teaching us some of the ins and outs of the program.

It’s fun to see girls leading the way with this technology. It’s also interesting to watch the students watch the printer. It reminds me of the 1950 ads for TV, where everyone sat around as close as they could. Yeah, that’s what’s happening in my class.

I can now see how I can incorporate this into my curriculum. How fun would it be to have students working together to create the digestive system? Fun right?! Or create geometric shapes based on specific dimensions. Or create an object with a specific volume. Or create a topographic representation of a state. The possibilities are endless. This is just the beginning, I can’t wait to see where this takes us!

What Common Core IS and ISN’T

There have been many jokes, comments, and criticisms against Common Core State Standards (aka Common Core/CC/CCSS). Many of them are made in ignorance; whether in not understanding the new standards or methods, I’m not sure. So let’s take a look at what Common Core is and isn’t.

What Common Core Is

Common Core is a group of standards (goals or objectives) that are set for all students. Some states have pulled out of Common Core, but still have their own state standards that are set for their students. CCSS simply states that for all students in Grade X, they will meet these objectives, regardless of where they live. So what 5th graders in CA are learning, is the same as what 5th graders in MI are learning. According to Common Core State Standards Initiative:

State education chiefs and governors in 48 states came together to develop the Common Core, a set of clear college- and career-ready standards for kindergarten through 12th grade in English language arts/literacy and mathematics. Today, 43 states have voluntarily adopted and are working to implement the standards, which are designed to ensure that students graduating from high school are prepared to take credit bearing introductory courses in two- or four-year college programs or enter the workforce.

Seems pretty benign, right? One would think so. So why all the hate? Some groups have twisted the facts, and money makers (i.g. textbook companies) have put their own spin on it.

What Does a Standard Look Like?

Here are some Language Arts and Math Standards at different grade levels:

  • 3rd Grade Language Arts: CCSS.ELA-LITERACY.RF.3.3.C
    Decode multisyllable words.
  • 7th Grade Writing: CCSS.ELA-LITERACY.W.7.7
    Conduct short research projects to answer a question, drawing on several sources and generating additional related, focused questions for further research and investigation.
  • 1st Grade Math: CCSS.MATH.CONTENT.1.NBT.C.6
    Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
  • 5th Grade Math: CCSS.MATH.CONTENT.5.NF.B.6
    Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

What Common Core Isn’t

It isn’t a Standardized Test – The high stakes testing came about during George W. Bush’s Presidency with the introduction of No Child Left Behind. It also tied test scores to sanctions against poor performing schools.

It isn’t a specific way of solving a math problem; a method – Yes, both examples of math standards (above) state two (2) ways to solve. HOWEVER, nowhere does it state that a student must draw a subtraction problem in one particular way. NOR does it state that there is one correct equation format. Ideally, a teacher models several methods and the student chooses the one(s) that is/are right for him/her. The idea is to have the students actively thinking and solving problems in various ways.

It isn’t the same – No longer are we teaching the ‘shortcuts’. For example, telling students to regroup or ‘borrow’ with a problem like: 34 – 19. No longer do we just say, ‘More on the top, no need to stop; More on the floor go next door‘ without explaining (and showing through various models) why. It’s now about the deeper understanding.

Still Against Common Core?

Which standard should your child NOT learn?

Common Core Is NOT Making Your Child Cry

What is Common Core?

Common Core simply refers to a group of standards. Standards are NOT new to education; they have been around for a long time. However in the past, each state had their own set of standards. So what one student learned in 5th grade in California was different than what another 5th grader was learning in Michigan. Independent state standards made more sense back when we, as a society, didn’t move around quite as much; and before we had a Global Economy and technology bringing us – not just states, but countries – together. As times have changed, so have our needs.

Here is a quality 3 minute video to explain it.

What Are the Common Core Standards?

Standards are goals that a child needs to meet at each grade level. Standards are NOT methods, curriculum (textbooks purchased by districts), or tests.

For example, one 3rd grade English Language Arts Standard states:

Use information gained from illustrations (e.g., maps, photographs) and the words in a text to demonstrate understanding of the text (e.g., where, when, why, and how key events occur).

That’s it, that’s the whole thing. I doubt anyone can argue that the above goal is a bad idea, or is making their child feel inadequate in any way. Okay, so most of the controversy centers around Math. I often hear statements like, “What’s wrong with the way I learned?” Well for starters, I’m guessing you have a base knowledge of how the actual function works. How many of us can explain why a fraction multiplied by aother fraction gives us a product that is less? We know, and can go through the motions of 1/2 x 1/3 = 1/6, but why? This is what Common Core is trying to have our students understand. There are LESS standards so that teachers can help students understand the WHY.

So let’s look at a 5th grade Math standard:

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Yes, all this states is that a student will add or subtract a fraction finding a common denominator. The wording is a bit different than that, but that’s what the standard states. Nowhere does it mention HOW it is to be taught – that would be a method, which are often found in curriculums. The key phrase in the standard is ‘equivalent fractions’. Why is this so important? Well, in the past we have taught students to find the common denominator by finding all the factors. There was very little time to explore that 3/6 is equivalent to 1/2 and 15/30. When students, and adults, are allowed to manipulate the information – via number lines or fraction tiles/bars – a better understanding is gained. Again, I doubt anyone really has an issue with the standard.

So What’s All The Fuss About?

It’s videos like this that focus on a method, and call it Common Core Math. Critics seem to focus on one method – arguably a long drawn out one to really drive home their message – and rant about its inefficiency. However, while watching this video I realized the ‘host’ and his explanation in the beginning are a perfect example of WHY we NEED Common Core, and illustrates our general lack of understanding. In the beginning, around the 8 second mark, he says that you, “Carry the 1,” when he is subtracting 3 from 5. Please notice that he stated, “Minus,” this is incorrect, the correct term is subtract. However, the bigger problem came when he explained that we needed to “Carry the 1”. Without getting too involved, what the problem has us doing is ‘regrouping’ (called ‘borrowing’ in my day). It is the actual process of taking a group – of 100 in this example – and placing it in the tens place. I wonder, without showing how ‘inefficient’ Common Core is, would he have been able to explain the why behind the actions? While many of those interviewed stated, “It takes too long” and “It’s too much work”, for those of us who have done it over several years, yes it’s not the best method for us. For those students just beginning to learn this standard, this method may be the key to success.

Critics have lost sight, maybe they never had it, that Common Core teaches VARIOUS methods. This kind of teaching allows ALL students access and understanding. Once a student has a firm grasp on the concept, they will move to our more traditional method, or more likely pull out their smartphone and use the calculator.

Why Are We So Frustrated?

Publishers and testing companies (consortiums as well) have muddied the waters. Publishers such as Eureka (Engage New York) and Pearson have taken it upon themselves to teach only certain methods. In addition, there have been several reports of misprints, thus causing MAJOR confusion with students and parents, in Eureka and Engage NY. Somewhere along the way, these publishers have decided what methods to teach, and we as teachers should do as they say. These companies are not looking out for the best methods, or interest, of our students. They are in it for a profit.

Another frustration, on the part of teachers, has been testing. We have been aware of Common Core standards for several years now. However, we were still bound to give state mandated tests, as stipulated under President Bush’s ‘No Child Left Behind’. This left teachers wanting to dig into the new standards, but as many of them did not line up with the state standards, Common Core was pushed to the back burner. We had tests to give, and proficiency levels to meet – which all boiled down to money, none of which made it to classrooms. There was little time for teachers to really grasp the full concept of the new standards. We were being pulled in many directions, then thrown into Common Core.

The Solution?

Brace yourselves…Get rid of testing and ditch the mandated curriculum. The curriculum are those books – teachers editions, student textbooks and workbooks – created by FOR PROFIT companies. I’m not saying that I shouldn’t be held accountable, by all means I should. There should be several ways in which a student is allowed to show mastery. A test given by the state, or a consortium, is not the answer. What about the student who can eloquently explain a process through a video, poetry, or interview? What if a rubric were designed and the student could SHOW their understanding this way? That is much more powerful that some test that is reduced to a number. Student want to show off their work and understanding, not show off some paper with a number printed on it.

More importantly, I am a professional. I went to school to become a teacher. I learned to create lessons WITHOUT a teacher’s manual. I can look at a standards and design a lesson to fit the needs of my students. This is what I went to school for! I am constantly refining my skills. These curriculums have hindered the teaching profession. They aren’t all bad, in some ways they are helpful. They help chunk and sequence how/when standards are taught. I have NEVER used a curriculum that has met the needs of every child/teacher. If I need help, then the curriculum should be a safety net, not the holy grail of math, language arts, or science. The companies and curriculums have sent an unconscious message that teachers are incapable of doing their jobs without them telling us what to do. Shame on them.

Who Is Making Your Child Cry?

Publishers and testing companies. And to be honest, they make me cry too. Instead of demonizing Common Core, and complaining how ‘time consuming’ a problem is, question the companies. Why do THEY feel this method is best, can a student use a method that is NOT approved by them, are these companies really needed? Celebrate the standards, just don’t confuse methods, curriculum, and testing with the standards.

Related Post: Why Common Core Is ‘Bad’