Three years ago Ron Ritchhart, from Project Zero introduced a thinking routine called Claim, Support, Question to me along with the rest of the MUS staff. He introduced it with a game called Sprouts. This simple routine has revolutionized my teaching. In a nutshell, Calm, Support, Question supports students in making conjectures or claims about anything they notices in their math lesson and guides them in proving or disproving those claims. This routine has created opportunities to make the students thinking visible and allows me as the teacher to identify misconceptions, deepen student conceptual understanding, and push student thinking far beyond the expectations of the content standards. Claim, Support, Question encourages students to behave like mathematicians and provides opportunities for students to develop the mathematical practice standards.

I presented how we use Claim, Support, Question at CMC South and CMC North with the game Werewolves in the Night. This year I have switched to using the game Poison to introduce the routine for a strategic purpose. Poison is a very simple two-person game played with 10 objects in a cup. Opponents alternate turns, taking either one or two objects out of the cup until all the objects are gone. The person who takes the last object is poisoned.

MUS has adopted a new curriculum. Like the game of Poison, on the surface many of the lessons look to be very simple. Also, like the game of Poison, when you provide opportunities for students to make claims and ask questions about things they notice, the levels of thinking, connection making, and conceptual understanding are endless. This can be true for any curriculum or lesson that is open ended and inquiry based.

With Claim, Support, Question I learned that:
• some 3rd grade students think that between 500 and 800 can only mean 650.
• some 5th graders believed it was coincident that 4.5 x 36 was equal to 45 x 3.6 even though they just got a 100% on their multiplying fractions unit test.
• some students believed that one game of Werewolves in the Night can be played for eternity.
• during a number talk, a 3rd grader claimed and supported with evidence that multiples of 6 also contain multiples of 2 and 3.
• that a math lesson can be so open ended and exciting if the teacher is willing to let it go in a strategic direction and has the math content knowledge to know where it is going.

Once teachers have invested time in teaching their students to make claims and support them with evidence, games, number talks, math lessons, and classroom discourse have never been the same.

http://www.cbsnews.com/news/parents-join-nationwide-boycott-of-common-core-exam/

The other day a parent shared with me this CBS story about parents boycotting the common core exam. I appreciate the press that our educational system is getting but wish it was more accurate. Based on this type of press and others like it in social media, I understand why anyone would oppose the common core. I on the other-hand do not. This is my response to the parent who sent me the video.

Thanks. I have not seen the video until today. I don’t have the same perspective as the woman in the video. As a parent, I am grateful that my children will be learning the curriculum outlined in the common core standards and not the retired California standards. I want my kids to grow up to be critical thinkers, sense makers, communicators, and problem solvers. These are all things that are brought out in the common core standards and were scarce in the retired California standards. With that said, there are many challenges we face with the transition to the new standards. The standards identify the content only. They do not identify the materials or instructional strategies. At MUS, as well with other districts, we are charged with identifying those strategies and materials in a very short time frame and in some cases having to develop our own as the transition period for common core is shorter than curriculum developers and trainers can keep up with. Common core is a change for teachers, students, and parents.

The common core is far from perfect. My biggest criticism of common core is the short transition period. The common core standards came out in 2010 but schools were held accountable to take the CST test which assessed the now retired California content standards until 2013. That means that most schools only had the 2013-2014 school year to completely revamp the content they taught, the curriculum, and the teaching strategies they use. In one academic year, teachers have been asked to undo what they spent at least a year of graduate school and many years of teaching mastering and totally revamp their role as a teacher. They have been asked to do this without all the supports they got when they first entered their career in education.

This change also has an impact on students. Students grew to learn that a good student sits quietly in class, listens carefully to the instructions and procedures of the teachers, and then quickly mimics those processes on their own. Now they are asked to try out their own ideas first, think about the ideas of others, and make sense of their learning. Kids never had to make sense of fractions or long division. Now they do. The hardest part of this change is students now have to make sense out of their current learning that builds upon their sense making from their past learning. The challenge is that the past learning they are building on did not have to make sense.

The CBS video has a particular focus on the testing of common core. I am not a fan of standardized testing and the need to rank schools by how well their students perform on a test. I do however appreciate the opportunity to see how much our children have grown and how they measure compared to their grade level expectations set by the common core standards. The parent in the video criticizes, “teaching to the test”. I believe that teaching to the test is a wonderful thing if we have the right test. The past California CST test did a great job of assessing how well students could select the correct multiple choice answer to a series of low level questions. Schools that taught to the CST test lowered their rigor as test taking strategies and the memorization of rules were more efficient than teaching students to think. With common core comes about a new type of assessment with few multiple choice questions and many opportunities for students to communicate their thinking and to analyze the thinking of others. If teaching to the common core test means that I have to teach my students to be critical thinkers, writers, and problem solvers then I support it. This is yet to be seen.

The mother in the CBS story also talked about how her 10 year-old child did not know what social studies was and listed that as another criticism of the common core. The common core standards actually promote more science and social studies as the language arts standards are explicitly connected to reading and writing in the content areas. Walk into any one of our classrooms at my school and chances are that most students would also say they don’t do social studies. They spend hours a day reading expository texts and writing about the impact of decisions on society. They debate, research, and respond to both past and current events. Is that language arts or is it social studies?

To conclude, I am grateful my 3 children will be educated in a common core world. I am grateful that we are educating our future workforce to be critical thinkers and sense makers. I wish educators and students would have another year or two before the high stakes testing begins to really strengthen our art of teaching. I wish curriculum developers had more time to really create better instructional materials rather than stick new labels on the old materials. I wish “the common core” did a better job of educating the public.

I first introduced number talks to my school a little over a year ago. With a few professional developments and resources, slowly they have expanded throughout our school. It is powerful to see students fluently solve problems with conceptual understanding, while using numbers flexibly and creatively.

Our guiding resource is Number Talks, by Sherry Parrish. I love this book and highly recommend it as a good starting point. It does a great job with developing understanding with addition, subtraction, multiplication, and division of whole numbers. Where the book falls short, is extending number talks into money, time, fractions, decimals, estimation, and patterns. Many of these ideas are picked up in the mini-lesson books found in Cathy Fosnot’s Context for Learning series.

Here are a few additional ideas:

Decompose a while number
The number 10 is composed of _____? (5 and 5, 2 and 8, 2 and 2 and 6,…)

Decompose a fraction
The number 7 ninth is composed of _____? (2 ninths and 5 ninths, 2 thirds and 1 ninth,….)

Decompose money
I have 45 cents. What coins might I have? (4 dimes and 5 pennies, 1 quarter and 4 nickels, ….)

Decompose time
At went to the park to play for 45 minutes. What did I do and how long did each thing take? (slide for 10 minutes, soccer for 30 minutes, and swings for 5 minutes)

Decompose a number with a decimal
The number 2.45 is composed of ______? (2 and .45, 1.45 and 1, four halves and .45)

Making change – Subtraction with money
If a spent $17.45 on ice cream for my family, what might my change be?
(If paid with $20 change would be $2.55, if paid with $18.00 change would be $0.55, if paid with $17.50 change would be $0.05,….)
OR I spent $17.45 on ice cream and paid with a $20 bill. What might my change be? (2 dollar bills, two quarters, and a nickel, or 10 quarters and a nickel,…)

Adding or subtracting fractions
1/3 + 1/2 + 1/8 + 1/4 + 1/8 =

Adding or subtracting time
School started at 8:30 and ended at 2:45. How long were you at school?

There are so many more places to talk number talks. Please share other ideas.

One of the most common questions I receive when I am working with a group of elementary math teachers is, “what does homework look like with this new way of teaching math?” To elaborate a bit more, when during class time, students are working on number talks and problem solving done with a group of students, how do we take that collaborative learning home?

Here are a few suggestions that are influenced by Lydia Song who put on a great workshop on extending and connecting number talks and problem solving.

Number Talk – Have the students do a number talk for homework with the directions, “solve the problem in two different ways. Show your thinking.” Below the two columns, have students explain one of their strategies and why it is an efficient way to solve the problem.
One of These Things – Students are given 4 numbers, pictures, or equations and need to explain why one of them is not like the others. The ultimate objective is for students to be able to provide mathematical reasoning for why each one of the 4 is different than the others.
Same, Same, Different – Copy 2 samples of student work from a number talk or problem solving side by side. Students then write about how the strategies are the same and how they are different.
Make it Easy- What number would you put in this equation to make it easier to solve? 39 + _____ + 46 = You can put any number in the blank. The key is to explain why did you select that number and why did that number make the problem easier to solve. “I would add a 1 to this problem because 39 and 1 makes 40 and 40 plus 46 is an easy problem to solve. 86” You can have the students answer each one of these in two different ways. “Another way is to add 5. I would add 5 because 4 goes to 46 to make 50 and 1 goes to 39 to make 40. 40+50= 90.” Or “I added 61 because 61 and 39 is 100 so 100+46=146.”
Which Strategy is More Efficient – This is set up the same as Same, Same, Different above with two student strategies put sided by side. The prompt is for students to analyze the work to determine which strategy is more efficient and why.

KEY CONSIDERATIONS
Homework gives parents a glimpse of what math looks like in the classroom. What message do you want to send parents? What message does a page of similar math problems on a worksheet send parents? Parents want to know what is happening at school so regular homework is important.

If students can’t do it at school, they can’t do it at home. If you have students solve 432 ÷ 12 = in at least two different ways for homework, be sure they have a variety of different strategies for solving similar problems in class first.

This is new to teachers, new to parents, and new to students. Be sure students have done similar assignments in class before they become homework. If a child goes home and says, “ I don’t understand what to do”, it often leaves parents with a negative perception of shifts in math education. With this in mind, I like the above homework ideas because they can become routine and problems and strategies can easily be swapped out to match the weekly content.

All of the above incorporate the standards of mathematical practice while building conceptual understanding and fluency.

This opinion, published on September 15 in USA Today sums up many of the key strengths of common core mathematics and clearly identifies what the standards are and what they are not.

http://www.usatoday.com/story/opinion/2014/09/15/common-core-math-education-standards-fluency-column/15693531/

Summertime is a time with lots of down time. There are many great educational apps that can be used to sharpen and learn new math skills throughout the summer. I plan on having my 6 year old daughter “play” on the ipad for at least 15 minutes a day on some of the following apps. Here is a list of some of my favorite math apps, what I like about them, and who could benefit from using them.

Dreambox –I love Dreambox because of all the different manipulatives it has students use (math rack, 100 chart, base ten blocks, area model, number lines,..) and because of its adaptive technology that moves you through the program based up the strategies you use and fluency with those strategies.
Cost- downloading the app is free but you either needs a school subscription (Montecito Union has a school subscription) or you can sign up as an individual for $12.99 a month or $19.99 for a family with up to 4 kids.
Grades- this app is great for kids entering kindergarten through 6th grade. They have just added a middle school component but I have yet to try it out. I am sure the math is great but don’t know if middle school kids will be as engaged as the younger ones.

Motion Math Pizza-This recommendation came from Dan Meyer’s blog post. In this game students run their own pizza business. They start with $50 and must buy ingredients, design pizzas, determine pricing, and sell pizzas. The customers’ interest and your profits are determined by the price points and menu options.
Cost – $3.99
Grades- I like this game for kids going into 3rd or up.

Numbers Logic Puzzle– This is one of my favorite apps. It is like playing Candy Crush but rather than matching up colors you match up number tiles that add up to ten. You can put together a 4 tile and a 6 tile, a 4 tile with a 1 and a 5 tile, or any number of tiles or combinations to make ten. Making ten is one of the most important number sense skills for any student.
Cost – Free
Grades- I like this game for kids going into 2nd or up.

Make 10 Plus– This app has a series of number tiles at the bottom of the screen that slowly rise throughout the game. Once the tiles reach the top of your screen the game is over. At the top of the screen is a number between 1-9. Students pick a number tile from the bottom of the screen that when added to the number at the top makes 10. This game promotes building fluency with making ten.
Cost – Free
Grades- I like this game for kids going into 1st or up.

Math Concentration– This is just like basic memory but with matching whole numbers, shapes, fractions, or multiplication facts to equivalent representations.
Cost – Free
Grades- I like this game for kids going into Kindergarten through 3rd grade.

Pick-a-Path– Help Okta reach the target by choosing a path from the top of the maze to the bottom. Seven levels with seven puzzles will test your skills with powers of ten, negative numbers, fractions, decimals, and more.
Cost – Free
Grades- I like this game for kids going into 4th grade and up.

Sudoku School– This sudoku app allows kids to do a 2×2 or a 6×6 sudoku game to gradually work their way up to a more challenging game.
Cost – Free
Grades- I like this game for kids going into 1st grade and up.

See other recommendations by grade level under the technology menu.

In the transition to common core students are being asked to go deeper by building conceptual understanding of the mathematics as well as know how to apply the math to real worlds situations. Students are being asked to do much more than just compute. I would suggest that this is an extremely challenging endeavor for everyone involved and one that is worth taking.

This transition away from memorizing procedures, formulas, and facts is forcing fundamental shifts in the classroom environment. Now outdated, is the teacher standing in front of the class at the whiteboard showing the class to just “invert and multiply” when dividing fractions, followed by students solving 1-47 odd of similar problems. International studies and the United States rankings in mathematics tell us what most of us have already discovered, this pedagogy has major limitations. Solving pages of problems that someone just showed us what to do does not allow for long-term retention beyond the test and is not the math we do in the real world.

Tied to this outdated system is the very simple way to identify and challenge those that were good at math. If a student was good at dividing a three-digit number by a two-digit number I could challenge that student by giving them the next page or by adding more digits to the problems that they solved. For those students that really needed the challenge, we could move them forward an entire chapter or even course. Although this satisfied many people’s need to show that their child is the highest or brightest, I question whether doing a skill earlier, faster, or with more digits is really more challenging.

Looking into our common core math classroom, you may see students working in groups with piles of cubes, building shapes on the latest ipad app, or collectively solving a mental problem at the white board. How can the kids that are good at math be doing the same thing that the rest of the class is doing and still be challenged? The answer is in the opportunities that the work provides and the willingness of the student to be challenged by those opportunities.

Some strategies that I love that promote thinking, conceptual understanding, and problem solving while challenging our top students include number talks, rich tasks or problems, 3-Act lessons, and Claim, Support, Question. Each one of these is worth it’s own attention to truly understand their value but they all share a few key connections. They each present the opportunity to see numbers at their pure form. Numbers can be broken in half, doubled, and reorganized to change the way you solve a problem. These strategies are open-ended and allow for the concept and understanding to go far beyond the mathematics of the grade level. Last, each of these strategies is less about the answer and more about the process and understanding to get the answer. The learning and the challenge happen in the process. The answer is a means to validate the process.

So, is my child being challenged? More than likely they are being challenged if they are being asked to persist, reason, construct, critique, and model. Probably not, if they are still solving pages of similar problems.

[Cross-posted from http://fawnnguyen.com/, Fawn Nguyen’s blog and mathbabe.org, Cathy O’Neil’s blog.]

Today’s post is an email interview with Fawn Nguyen, who teaches math at Mesa Union Junior High in southern California. Fawn is on the leadership team for UCSB Mathematics Project that provides professional development for teachers in the Tri-County area. She is a co-founder of the Thousand Oaks Math Teachers’ Circle. In an effort to share and learn from other math teachers, Fawn blogs at Finding Ways to Nguyen Students Over. She also started VisualPatterns.org to help students develop algebraic thinking, and more recently, she shares her students’ daily math talks to promote number sense. When Fawn is not teaching or writing, she is reading posts on mathblogging.org as one of the editors. She sleeps occasionally and dreams of becoming an architect when all this is done.

Importantly for the below interview, Fawn is not being measured via a value-added model. My questions are italicized.

——

I’ve been studying the rhetoric around the mathematics Common Core State Standard (CCSS). So far I’ve listened to Diane Ravitch stuff, I’ve interviewed Bill McCallum, the lead writer of the math CCSS, and I’ve also interviewed Kiri Soares, a New York City high school principal. They have very different views. Interestingly, McCallum distinguished three things: standards, curriculum, and testing.

What do you think? Do teachers see those as three different things? Or is it a package deal, where all three things rolled into one in terms of how they’re presented?

I can’t speak for other teachers. I understand that the standards are not meant to be the curriculum, but the two are not mutually exclusive either. They can’t be. Standards inform the curriculum. This might be a terrible analogy, but I love food and cooking, so maybe the standards are the major ingredients, and the curriculum is the entrée that contains those ingredients. In the show Chopped on Food Network, the competing chefs must use all 4 ingredients to make a dish – and the prepared foods that end up on the plates differ widely in taste and presentation. We can’t blame the ingredients when the dish is blandly prepared any more than we can blame the standards when the curriculum is poorly written.

Similary, the standards inform testing. Test items for a certain grade level cover the standards of that grade level. I’m not against testing. I’m against bad tests and a lot of it. By bad, I mean multiple-choice items that require more memorization than actual problem solving. But I’m confident we can create good multiple-choice tests because realistically a portion of the test needs to be of this type due to costs.

The three – standards, curriculum, and testing – are not a “package deal” in the sense that the same people are not delivering them to us. But they go together, otherwise what is school mathematics? Funny thing is we have always had the three operating in schools, but somehow the Common Core State Standands (CCSS) seem to get the all the blame for the anxieties and costs connected to testing and curriculum development.

As a teacher, what’s good and bad about the CCSS?

I see a lot of good in the CCSS. This set of standards is not perfect, but it’s much better than our state standards. We can examine the standards and see for ourselves that the integrity of the standards holds up to their claims of being embedded with mathematical focus, rigor, and coherence.

Implementation of CCSS means that students and teachers can expect consistency in what is being in taught at each grade level across state boundaries. This is a nontrivial effort in addressing equity. This consistency also helps teachers collaborate nationwide, and professional development for teachers will improve and be more relevant and effective.

I can only hope that textbooks will be much better because of the inherent focus and coherence in CCSS. A kid can move from Maine to California and not have to see different state outlines on their textbooks as if he’d taken on a new kind of mathematics in his new school. I went to a textbook publishers fair recently at our district, and I remain optimistic that better products are already on their way.

We had every state create its own assessment, now we have two consortia, PARCC and Smarter Balanced. I’ve gone through the sample assessments from the latter, and they are far better than the old multiple-choice items of the CST. Kids will have to process the question at a deeper level to show understanding. This is a good thing.

What is potentially bad about the CCSS is the improper or lack of implementation. So, this boils down to the most important element of the Common Core equation – the teacher. There is no doubt that many teachers, myself included, need sustained professional development to do the job right. And I don’t mean just PD in making math more relevant and engaging, and in how many ways we can use technology, I mean more importantly, we need PD in content knowledge.

It is a perverse notion to think that anyone with a college education can teach elementary mathematics. Teaching mathematics requires knowing mathematics. To know a concept is to understand it backward and forward, inside and outside, to recognize it in different forms and structures, to put it into context, to ask questions about it that leads to more questions, to know the mathematics beyond this concept. That reminds me just recently a 6th grader said to me as we were working on our unit of dividing by a fraction. She said, “My elementary teacher lied to me! She said we always get a smaller number when we divide two numbers.”

Just because one can make tuna casserole does not make one a chef. (Sorry, I’m hungry.)

What are the good and bad things for kids about testing?

Testing is only good for kids when it helps them learn and become more successful – that the feedback from testing should inform the teacher of next moves. Testing has become such a dirty word because we over test our kids. I’m still in the classroom after 23 years, yet I don’t have the answers. I struggle with telling my kids that I value them and their learning, yet at the end of each quarter, the narrative sum of their learning is a letter grade.

Then, in the absence of helping kids learn, testing is bad.

What are the good/bad things for the teachers with all these tests?

Ideally, a good test that measures what it’s supposed to measure should help the teacher and his students. Testing must be done in moderation. Do we really need to test kids at the start of the school year? Don’t we have the results from a few months ago, right before they left for summer vacation? Every test takes time away from learning.

I’m not sure I understand why testing is bad for teachers aside from lost instructional minutes. Again, I can’t speak for other teachers. But I do sense heightened anxiety among some teachers because CCSS is new – and newness causes us to squirm in our seats and doubt our abilities. I don’t necessarily see this as a bad thing. I see it as an opportunity to learn content at a deeper conceptual level and to implement better teaching strategies.

If we look at anything long and hard enough, we are bound to find the good and the bad. I choose to focus on the positives because I can’t make the day any longer and I can’t have fewer than 4 hours of sleep a night. I want to spend my energies working with my administrators, my colleagues, my parents to bring the best I can bring into my classroom.

Is there anything else you’d like to add?

The best things about CCSS for me are not even the standards – they are the 8 Mathematical Practices. These are life-long habits that will serve students well, in all disciplines. They’re equivalent to the essential cooking techniques, like making roux and roasting garlic and braising kale and shucking oysters. Okay, maybe not that last one, but I just got back from New Orleans, and raw oysters are awesome.

I’m excited to continue to share and collaborate with my colleagues locally and online because we now have a common language! We teachers do this very hard work – day in and day out, late into the nights and into the weekends – because we love our kids and we love teaching. But we need to be mathematically competent first and foremost to teach mathematics. I want the focus to always be about the kids and their learning. We start with them; we end with them.