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.

The most common question I have received from parents recently is, “how do I support my child with their new type of homework?” I am often tempted to use the words of Dan Meyer, to “be less helpful”, but know that has the potential to be misconstrued. The heart of Dan Meyer’s words is the need for students to experience productive struggle. I recently received an article titled, “What are the Characteristics of a Good Math Teacher?” I think this article does a good job of capturing this important message for both teachers and for parents.

What are the Characteristics of a Good Math Teacher?

Posted on February 18, 2014 by Dave Youngs
www.aimsedu.org

When asked to pick the two most important characteristics of a good math teacher many people usually say being able to explain math well and showing how to do problems.

Research shows that these two things can actually hinder mathematics learning. Both of these traits foster an unintended consequence—a learned helplessness in math. The unwritten message students get is that math is hard and that they can’t do it without the teacher explaining it well and showing them how. These two traits have a negative impact since they unwittingly encourage students both to play a passive role in learning mathematics and to give up before expending much effort—knowing that the kind teacher will come to their aid and show them how to do the problems.

Brain research has found that when students actively engage in problem solving they create new neural pathways. The key is to pose problems or tasks that are just beyond the current abilities of the students so that the students are stretched, but not overwhelmed. Any aid the teacher gives is limited to helping students make sense of the problems and encouraging the students to persist in solving the problems instead of showing the students how to do so. This approach embodies the first Common Core Standard for Mathematical Practice—make sense of problems and persevere in solving them.

When students are not shown a step-by-step procedure for solving a problem, they are forced to think for themselves. This fosters a mindset in students that math may be hard, but if the students work diligently they can learn it.

A good math teacher is one who poses problems that stretch her students’ thinking and then supports their efforts—instead of being a good explainer and helper who carefully shows students how to do math.

San Francisco Chronicle
Thursday, January 9, 2014

Math is getting a major makeover.

By fall, traditional textbooks mostly will be tossed aside in California classrooms. What’s taught in each grade will get shuffled around and, often, merged. First-graders will get tiny tastes of algebra while learning to add, and middle school students will be exposed to statistics and geometry while still solving for X.

The changes are part of a national shift to Common Core standards, which identify the skills and topics to be taught at each grade level, with a focus on critical thinking and real-world applications rather than rote memorization.

So far, 45 states, including California, have agreed in the past few years to switch to the new standards, creating a more cohesive national public education system. The effort has been coordinated by the National Governors Association and the Council of Chief State School Officers.

The new system, according to proponents, will offer a more logical progression of math concepts and include real-life reasons for learning, say, about exponents or linear equations, local and state education officials said.

To be sure, 1 plus 1 will still equal 2 under the new standards. But the changes are creating some apprehension among parents trying to figure out why the course called Algebra I is disappearing from middle schools, and what it means for math-whiz kids who want to take calculus someday or students who might not be ready for bivariate data analysis before puberty hits.
Bigger changes

In San Francisco, Deputy Superintendent Guadalupe Guerrero is leading the changes, making sure math teachers know what to teach and how to teach it, even without new textbooks or a set teacher manual.

He has two words of advice for perplexed parents: “Don’t panic.”

This isn’t the first time math has gotten an overhaul in public schools.

In the 1960s, there was the much-criticized new math, which included set theory and number bases other than 10. That was scrapped eventually, replaced by the old math. And then, in 1975, there was the mandated switch to the metric system – a change beat back inch by inch.

This is bigger.

“I think it’s huge, actually,” said Brooke Arroyo, an eighth-grade math teacher at Denman Middle School in San Francisco.

Arroyo teaches Algebra I but is transitioning to the new system, which would have most eighth-graders taking a course called Math 8 or something similar, depending on the district.

To many parents and students, that might sound like an easier course. It won’t be, Arroyo said.
Local flexibility

“I think there’s a lot on labels, and I can understand that people think it’s being dumbed down,” she said. “Eighth-grade math is going to have geometry in it and algebra. It’s just not going to be called algebra. It’s not going to be called geometry.”

While the Common Core standards ensure that students in the same grade will be learning basically the same content whether they live in Minnesota, Kansas or California, there is local flexibility to adjust courses or content to accommodate both struggling and advanced students.

In Oakland, the school board is expected to vote this month on a middle and high school course sequence that offers advanced students the ability to combine Math 8 and Algebra I in eighth grade and then head into geometry in ninth grade.

The plan also offers students a second chance to merge Algebra II and math analysis in their sophomore or junior years. Both options allow students to reach Advanced Placement Calculus as juniors or seniors, as they can now.

Struggling students could see a supplemental math class on their daily schedule.

“We’re trying to keep all those options open,” said Phil Tucher, administrative manager of mathematics for Oakland Unified. “We don’t want people to perceive that we’re slowing down mathematics.”

The new Oakland plan ensures that advanced students don’t miss any content even if they choose an accelerated option. Currently, students who excel in math often skip a course – pre-algebra, for example – to reach calculus in high school. Many struggle to keep up or maintain grades because they don’t have a solid foundation in the basics, Tucher said.

San Francisco plans to offer similar options.

Making the switch to the Common Core hasn’t been easy, especially in math.
Textbooks lag behind

While the national standards tell schools what to teach and when, the how is left completely up to states, districts or even schools.

Schools have some flexibility in what content they teach, but standardized tests – which can be linked to funding and staffing – will be based on the new standards.

“Typically, you might open your textbook and go cover to cover,” said Guerrero of the San Francisco Unified School District.

But there aren’t official textbooks yet. Publishers are just starting to push out new materials, but in many districts, including some in the Bay Area, teachers and curriculum experts are creating their own and sharing them across the country via online forums and Google Drive.

“Here at Denman, teachers are not holding tight to the textbooks,” said Ann Lyon, the middle school’s instructional reform facilitator. “It’s an exciting challenge to come up with the kind of activities that are engaging to students.”

Those activities will look much different from the solve-for-X problems that typically come at the end of textbook chapters.

At Denman, under the Common Core, eighth-grade students might have to estimate a wildlife population using colored Goldfish crackers, an activity that uses algebraic functions, proportion and estimation, with a built-in snack at the end, Lyon said.

Yet getting everyone up to speed will take time – and there’s not a lot left.

The first round of standardized testing based on the Common Core will happen just more than a year from now.

But teachers can’t toss out the old textbooks quite yet.
Filling the gaps

Common Core math classes build on the content that students learned the previous year. And since seventh-grade students, for example, didn’t grow up under a Common Core background, there will be gaps in what they need to know to understand the content or to do well on the new state tests.

Teachers will have to fill in the blanks to ensure their students are ready for the Pythagorean theorem as well as roots and exponents in the eighth grade.

Oakland schools expect to be rid of Algebra I in middle schools and fully implementing Common Core by next fall. San Francisco officials are hoping to get there as well, but they are still assessing the district’s readiness.

In the meantime, like many parents, San Francisco dad Todd David is crossing his fingers that everything will work out when it comes to his son’s math classes.

“In general change is hard,” said David, whose child is a sixth-grader at Everett Middle School. Successful implementation will probably vary school to school and even teacher to teacher, he said. “To me it comes down a little bit to the luck of the draw.”

Jill Tucker is a San Francisco Chronicle staff writer. E-mail: jtucker@sfchronicle.com

http://www.sfgate.com/education/article/Number-of-major-math-changes-for-California-5125879.php#page-1

In the spirit of the holiday season, when looking for a gift for a young child, teenager, or adult, consider the giving a jigsaw puzzle. Puzzles are one of many toys that allow opportunities for mathematical concepts to emerge during play. Some of those opportunities include children seeing how a picture is composed of smaller pieces and then eventually decomposed from a complete picture back to smaller pieces.

In our shift to common core standards, a major emphasis is being placed on the standards of mathematical practice. Puzzle building presents a great way to teach perseverance as children progress to puzzles with 100 or more pieces that can take hours or days to complete (Math Practice 1). Puzzle building also requires children to make use of the structure of a puzzle (Math Practice 7). Does the piece contain a smooth edge? Does it have unique characteristics? What colors do you see on the piece? This leads to sorting and classifying pieces in a way that makes sense to the puzzle builder.

One important thing to consider is picking the right puzzle for the child. Consider the person’s interest, as it may be Batman or ponies that first gets a child to buy-in to building their first puzzle. Also consider the child’s ability and experience with puzzles. The quickest way to turn off puzzle building interest in a child is to give them a puzzle that is way beyond their ability. Consider starting easier if you are unsure. Sometimes, early success could promote future interest.

Puzzle away!

I was introduced to Dreambox learning, an on-line learning program, while attending a session lead by Cathy Fosnot in Palm Springs. I figured it was just another program that paid a big name to promote their site. I signed up for a 30-day trial for my school, which the 2nd grade team was happy to try out. I also did some research with my 5 year old daughter Emilia. The game was a hit. Soon, the kindergarten and 1st grade teams got word of the excitement and were interested in trying the game. It has since grown to included 3rd and 4th grade. Although most classrooms have only tried the game a few times, I see many benefits to using the game as part of our mathematics program. First, it is easy to access. Students can log in from home or at school using a computer or ipad with internet access. The game is adaptive based upon the strategies the students use to solve a problem, how long it takes to solve a problem, and the answer they provide. As a math specialist, I love that the game has students working with number lines, hundreds charts, math racks, ten frames, and other concept building digital manipulatives. Most importantly, the students are highly engaged with the game and continue to ask for more time playing it at school and how they can access it from home.