Peer Observation to Impact Learning

More and more, administrators and teachers are viewing peer observation as a form of collaborative professional development. This kind of observation can yield its greatest benefits when used as a means of sharing instructional techniques and ideologies between and among teachers.
Most important to effective teacher observation is that it be student-focused. The emphasis needs to be on how things can be done differently in the classroom to ensure that students succeed academically.
Kindergarten teachers at Paine Primary have been spending valuable time visiting each other's classrooms in order to learn from each other. Everyone benefits from this practice of "shared refining" of their craft.
Teachers benefit from:
 * an opportunity to engage in reflective dialogue about their work.
 * the focused classroom support.
 * improvement of classroom practices.
 * support from a peer who understands the daily demands of the classroom.
 * satisfaction with one's work.
 * reduced job stress, especially for the new teacher.
 * a welcoming atmosphere for new teachers.
 * the comfort of knowing that someone is available to help, explain, and assist.
The school benefits from:
 * increased collaboration among teachers.
 * the establishment of a professional learning community.
 * an increased focus on student achievement.
 * enthusiasm for the teaching profession.

Excerpts from post- Source: http://www.educationworld.com/a_admin/admin/admin297.shtml
"Teachers Observing Teachers: A Professional Development Tool for Every School"

We Are "Falling" For Math At Paine Elementary K-2

Learning Targets- Aiming for Understanding

Learning targets, as their name implies, guide learning. They describe, in language that students understand, the lesson‑sized chunk of information, skills, and reasoning processes that students will come to know deeply. We write learning targets from the students’ point of view and share them throughout the lesson so that students can use them to guide their own learning. Finally, learning targets provide a common focus for the decisions that schools make about what works, what doesn’t work, and what could work better.

Daily Learning Targets around Paine Elementary K-2:

Math Around Paine Elementary K-2

Math is all around the Paine Elementary K-2 building! Students have been talking about the characteristics of mathematicians. They learned that they are all mathematicians! Students are using graphing skills to get to know each other. They counted the letters in their name and used number paths and ten frames to show the number. 

It’s the beginning of the new school year, so what better time to think about the time-honored tradition of counting to the 100th Day of School? Many teachers have routines for counting the days to the 100th day, but I want to propose using ten-frames.  You can address a number of  Kinder and 1st grade standards with this simple daily routine!

Just print out  blank ten-frames, grab yourself some colored Avery sticky dots, and you’re ready to go. Be sure to use either one color of dots, or vary the color in groups of 5 to help students subitize groups of 5 and 10 on the ten-frames.

Questions for Whole-Group Lessons:

There are so many directions you can take your questioning. To help you better visualize how the conversations might go, I’ve used the number 47 in this example:

•How many days have we been in school? (47) How do you know it’s 47? (The 4 tens are 40, then I saw 5 and 2 more, so that’s 47)
•Describe 47 using tens and ones. (4 tens and 7 ones) Can anyone describe it a different way? (3 tens and 17 ones, 2 tens and 27 ones, 1 ten and 37 ones, or 47 ones)
•How many more days until we reach 50 days (3). How do you know? How many more until the 100th day? (53) How do you know?
•What’s one more than 47? (48) What’s one less than 47? (46)
•How would we write 47 in expanded form? (47 = 40 + 7)
•Let’s start at 17 and  count around the circle until we get to 47.

5 Principles of Extraordinary Math Teaching

1. Give students time to struggle

Students learn by grappling with mental obstacles and overcoming them. Your students MUST spend time stuck on problems. The more a teacher steps in to solve a student’s problems, the less the student learns. This is not to say you shouldn’t be involved in their process at all. Learn how to identify when your students are productively stuck—i.e. unable to answer the question but still making progress by making various attempts at understanding the problem—and when they are unproductively stuck—i.e. giving in to despair and hopelessness about the problem.
Productively stuck students need little more than a bit of encouragement, reflection, or the occasional prompt from a teacher (best offered in the form of a question, such as “What have you done so far?” or “Have you tried ____?”). Unproductively stuck students need help scaffolding the problem, by rephrasing the question, identifying learning gaps, and possibly backing up to a more concrete or simpler problem. For both, time is critical: prioritize giving students the time required to let their perseverance flower.

2. Say yes to your students’ ideas

Doing math is creative work. It requires making connections between distinct concepts, translating knowledge into new contexts, and making intellectual leaps into unexplored territory. These are the hallmarks of creative thinking, and this is exactly the kind of capacity we want our students to develop. Creative work is hard, though, and becomes especially hard when the process of creative work is received with skepticism and negativity. When a student is working on a hard math problem, they are in a delicate place full of uncertainty, and a lot of the time the ideas they will have are wrong, or at least not exactly right. Many teachers want to point this out immediately to a student who is tentatively putting forth what to them is a novel idea on how to make sense of a math problem. However, to have an idea shut down means the student misses out getting to see why their idea might or might not work, and more importantly, they miss out on the exciting process of following wrong ideas into deeper understanding. We want our students to practice coming up with ideas and following them, even down rabbit holes, to see what they can discover.
As a teacher, one of the best ways to support the creative growth of students is to say yes to their ideas. That doesn’t mean confirming the correctness of an idea, but it does mean refraining from pointing out the wrongness. Instead, encourage students to test out their ideas for themselves. Say yes to the creative act and respond “I don’t know—let’s find out!”

3. Don’t be the answer key

Most students will avoid hard work if they suspect there is an easier way. (Most people do this too. It’s an efficient strategy for handling a complex world with an abundance of information.) Unfortunately, there is no substitute for hard work when developing the mind. Students need to struggle with concepts themselves if they are going to understand or master them. They will not struggle if they believe that instead, they can ply the teacher for the answer. The teacher needs to avoid being seen as the source of all knowledge in the classroom.
Rather, the teacher is the orchestrator of the classroom, setting up learning opportunities in which the students come to possess their own knowledge through grit, patience, and hopefully joy. Instead of using your knowledge to confirm to students when they have answered a problem right or wrong, encourage students to reference their own understanding of the problem and the mathematics behind it. If they don’t have the conceptual models at hand to check their understanding, help them build what they need.

4. Questions, questions, questions

Practice asking questions. Practice launching your lessons with questions and interacting with your working students by posing questions. Give your students opportunities to ask questions, and find ways to show them you value their questions. You can do this by using their questions to guide a lesson, having a special “Questions” board in the classroom, or making time for students to think of and write questions in a math journal.
Not all questions will be answered, and that’s okay. (You are not the answer key, remember?) More important than answering all the questions is learning the practice of asking them in the first place. Students benefit from having the classroom be a place of questions. Questions keep the math classroom active, engaging, and full of surprises. For many students, developing the habit of asking questions about math, and seeing the teacher ask questions about math, marks the point in their elementary math lives when math truly comes alive.

5. Play!

Seriously. The more a teacher models a positive and excited disposition toward learning and especially mathematics, the more students will begin sharing in the fun. Find the parts of math that you love, and share your joy with the students. Look for opportunities to keep play at the center of the classroom: for example, introduce games to students by playing them (rather than just explaining them); give students an opportunity to play freely with math manipulatives; and be willing to play along when students try changing the rules of a game to invent their own variation.
Avoid false enthusiasm: students know the difference. Find out how to get excited about math, and give yourself permission to play. Maybe for you this means being attentive to patterns, or finding really juicy questions to start a lesson with, or spending time making your own mathematical discoveries (remember how good an aha! moment feels?). Develop your own relationship with math and your students will benefit.

From the blog Math 4 Love
link: http://mathforlove.com/

Math Anxiety

The Family Roots of Math Anxiety

By Sarah D. Sparks on August 10, 2015 11:23 AM

In general, parents' help with homework can be a major support for students. But if parents shudder at the thought of algebra or arithmetic, they can pass that math dread on to their children.

So finds the latest in a series of studies by University of Chicago psychologists including Erin Maloney, Sian Beilock, and Susan Levine, who study the causes and effects of performance anxiety. The new research, in the journal Psychological Science, finds that parents with math anxiety can hinder their students' progress in math.

The researchers tracked more than 400 1st and 2nd grade students whose parents provided different levels of help with their homework. They also assessed both parents' and kids' attitudes toward math at the beginning and end of the school year.

Students whose parents reported high math anxiety made significantly less progress in math over the course of a year, and they were more likely to become anxious themselves—but only if their anxious parents sweated through helping them with homework.

By contrast, students with math-anxious parents who helped with homework showed no similar problems when it came to reading. While there may also be some genetic influence on math anxiety, that did not seem to be a factor here. Students whose anxious parents did not help with math homework did not show similar difficulties or fear when it came to math.  

Parent Attitudes Shape Children

Even if a parent understands how to do a problem, his or her underlying dread of math could hinder students' enjoyment of solving problems, particularly if it plays into broader stereotypes about who should like or be good at math.

"Our work suggests that if a parent is walking around saying 'Oh, I don't like math,' or 'This stuff makes me nervous,' kids pick up on this messaging and it affects their success," Beilock said in a statement.

That's in line with prior research that found girls whose female elementary teachers were anxious about their own math competence showed bigger gender gaps in math performance by the end of the year, even if they had started on par with boys. Maloney told me that because nearly 9 out of 10 parents who responded in this study were women, they were unable to look at parent gender differences, but they found no differences in the effects of parent anxiety on boys versus girls. 

Overcoming Dread of Numbers

Even if parents try to control how they talk about math, fear may hinder how they help their children, the researchers found. Anxious parents may have trouble explaining math concepts, Levine noted in a statement. They may react badly when their children make mistakes while solving a problem. 

"We can't just tell parents—especially those who are anxious about math—'Get involved,'" Maloney said in a statement on the study. "We need to develop better tools to teach parents how to most effectively help their children with math."

We already see this for teachers. One school in New York, for example, offers weekly training to help math-anxious teachers brush up on skills and gain confidence with numbers. Another works with teachers to understand the theory of growth mindset—that math performance is not a fixed innate skill, but one that can be improved through effort.

Photo Source: Getty Images

Number Talk Training

Teachers from Paine Primary recently attended a Number Talk workshop. A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply, and divide.  
Pictured are teachers Catherine Finkley, Penny Moore, Emily Wolfe, and Cynthia Weyerman. 

Math Practice Standards in All Subject Areas

As a math teacher, I would ask my students to write. They would complain that it was math class and they should not have to write in math. I would tell them that there's no such thing as "math day" out in the real world. Outside of school, math is integrated into everyday tasks and work tasks. While numbers in isolation are rarely useful, writing about what the numbers mean is important for clearly communicating ideas.
Mathematics is modeled in almost any field. Common Core standards ask students to do research, look at real-world contexts, make sense of the world around them, and be able to reason and justify conclusions. The eight Common Core Standards for Mathematical Practice can be applied in any subject area. Here are some suggestions for how we can all be teachers of the Common Core math standards:

1. Make sense of problems and persevere in solving them. (CCSS.MATH.PRACTICE.MP1)

Any subject area can ask students to make sense of problems. Rather than giving students step-by-step instructions where everyone's outcome is the same, pose an interesting problem or question for students to figure out the solution. The problem does not have to be a math problem -- every subject has things that students can figure out. The solutions need to be more than a quick answer. To persevere, students should work their way through solving a multi-phase problem. The answer to one part becomes information they'll need to answer the next part.

2. Reason abstractly and quantitatively. (CCSS.MATH.PRACTICE.MP2)

Use numbers to reason. All subject areas have data that can be analyzed. If teachers are posing DOK 3 and DOK 4 problems, students need to look at evidence, make sense of it, and draw conclusions. This is done with textual evidence as well as numerical data. Have students analyze the water crisis in California. Part of that is looking at the data on rainfall, crop irrigation needs, farmers' crop outputs, household water use, etc. Every class should have students looking at this data, analyzing it, making charts, and drawing conclusions.

3. Construct viable arguments and critique the reasoning of others. (CCSS.MATH.PRACTICE.MP3)

Piggybacking on the previous standard, students should defend their arguments with data that they've reviewed. Viable arguments don't have to be about numbers. Every subject should have students construct an argument. Doing peer evaluation allows each student to critique others and defend his or her own reasoning. Students can also critique the reasoning of authors of texts. This can be done in any class.

4. Model with mathematics. (CCSS.MATH.PRACTICE.MP4)

Math is present in everyday applications. How does your subject area utilize math? Whether in art, music, history, economics, or science, we all have uses for math. How are math concepts represented in your subject area? Make an effort to expose your students to the ways in which your subject area models math.

5. Use appropriate tools strategically. (CCSS.MATH.PRACTICE.MP5)

When students are faced with a problem, do they realize that they need to utilize a ruler, protractor, computer, or spreadsheet to solve it -- without your telling them? All classes can use spreadsheets to organize information. Tools do not need to be math tools specifically. In the course of their everyday lives after graduation, students will need to decide whether they should they use a text document or spreadsheet, create a flowchart or timeline, use one of many collaborative or web 2.0 tools, or punch numbers into a calculator. Now is their chance to learn the best strategic use for these tools and many others.

6. Attend to precision. (CCSS.MATH.PRACTICE.MP6)

Students tend to give vague answers, so we must work with them to be specific and back up their statements with evidence. This evidence doesn't have to be with mathematical numbers. When dealing with data and numbers, students should be able to come up with a precise answer whenever it is required.

7. Look for and make use of structure. (CCSS.MATH.PRACTICE.MP7)

Every world language has patterns and structure for students to observe and analyze. Looking for patterns and structure in history should already be occurring. In any subject area, students could be seeking patterns and structure to give them a deeper understanding of a problem.

8. Look for and express regularity in repeated reasoning. (CCSS.MATH.PRACTICE.MP8)

All students should be continually evaluating the reasonableness of their intermediate results. Throughout the process of solving any problem (not just a math problem), students look for things that repeat. When writing an essay, they're using a similar structure throughout the writing process.
As you construct your lesson plans, consider which of these eight mathematical practices you can include. Quite possibly, you're already including some of the practices in your Common Core lessons. If we want to strengthen students' reasoning and numerical literacy skills, we can't just relegate the mathematical concepts to math class. The more cross-curricular thinking we apply to our lesson plans, the more opportunity students will have to find value in what they're learning.

How do you use the Common Core math standards?


Alice Keeler is a Google Certified Teacher, New Media Consortium K12 Ambassador, Microsoft Innovative Educator and LEC Admin & Online and Blended certified. Professor of Curriculum, Instruction and Technology at California State University Fresno and Teacher on Special Assignment at ACEL Charter High school. Alice Keeler has developed and taught online K12 courses as well as the Innovative Educator Advanced Studies Certificate (cue.org/ieasc). A believer in the importance of connectivity she founded #coffeecue (cue.org/coffee) and #profchat. Masters in Educational Media Design and Technology. Doctoral student at Boise State University in EdTech with a focus on gamification. Passionate that kids are not failures, using technology to change the way we approach learning and grading. Alice tweets @alicekeeler and blogs at alicekeeler.com.

Teachers Participate in OGAP (Ongoing Assessment Project) for Math

Paine Primary math coach, Donna Brumlow and teachers Gina Lackey, Donna Walker, Jeanette Cerisano, Kay Shumate, and Beth Ann Marshall recently participated in OGAP training with other regional coaches and teachers.

The OGAP formative assessment system is based on the belief that teachers make more effective instructional decisions resulting in improved student learning when they: (a) are knowledgeable about how students develop understanding of specific mathematics concepts and about preconceptions and misconceptions that interfere with learning these concepts; (b) have tools and strategies that allow them to systematically monitor their students’ understanding prior to and during instruction; and (c) receive professional development focused on that knowledge, those tools, and those strategies. Four principles about effective instruction and assessment underlie OGAP’s design:

1. Build on students’ pre-existing knowledge. Ignoring students’ initial thinking risks students developing understandings that do not match what the teacher intended (NRC, 2001b).
2. Teach (and assess) for understanding. Because teaching for understanding “improves retention, promotes fluency, and facilitates learning related materials” (NRC, 2001b), OGAP items and tools are designed to elicit conceptual understanding.
3. Use formative assessment intentionally and systematically. Research has shown that learning gains from systematically implementing formative assessment strategies into instruction are larger than gains found for most other educational interventions (NRC, 2001a).
4. Build assessments based on the mathematics education research. A key recommendation from Knowing What Students Know (NRC, 2001a) is that assessments should be built on research on how students learn specific mathematics concepts.

OGAP is both a product and a process: professional development focuses on research about how children learn mathematics, providing a rationale for the design of the item bank and frameworks. It also shows teachers how to use those tools, and models routines that allow them to use them well.

Source: http://www.cpre.org/ogap

Math Curriculum Day 2015

Teachers from Paine Primary gathered on June 25th in order to become familiar with the components of our new curriculum, Eureka Math. Teachers were given in-depth professional development during the morning session. The second portion of the day was devoted to collaboration with grade level planning partners to discuss implementation of Module 1.

3 Positive Things About College and Career Ready Standards

Posted by Lindsey Walborn on Wednesday, 06/17/2015

1. Learning progressions

The CCSS do a great job of building learning progressions through all K-12 grade levels so that each year students build on what they learned the year before and deepen those skills. One example is equations. In kindergarten through second grade, students use equations to represent addition and subtraction problems. This includes the decomposition of numbers in multiple ways (8 = 4+4 and 8 = 3+5), finding the missing number in an addition equation (3 + __ = 8), and writing equations from visual representations and word problems. In grades 3-5, these same ideas are extended to multiplication and division.  

As students move into middle school, variables (x, y, z) are added to equations, and students use opposite operations to find the variable’s value. For example, students are asked to solve 3x + 4 = 8 for x. Students also learn equations in two variables where the result is a straight line graph (y = 3x - 2).

As students move through high school, their understanding of the concept of functions grows to include exponential (think money growing in your bank account), quadratic (functions that model the motion of an object being thrown in the air), and other types. This comprehension of math as it relates to real-world phenomena wouldn’t be possible without the basic understanding that the two sides of an equation are equal, which was established in elementary school.

2. Focusing not only on the how… but the why

I created this Wordle using the top 100 words in the CCSS math standards. The bigger the word, the more frequently it appears in the standards.   

When this picture popped up, I was surprised at the sentence that emerged: “Understand problems using numbers and equations.” This is the foundation of the Common Core math standards. We want students to truly understand mathematics, not just be able to “do” it.  

I also couldn’t help but notice the words that are not visible in this picture, such as do and compute. While there is a place in the standards for algorithms, such as putting numbers on top of one another and adding down, it’s not the focus. Other visible words that support the idea of understanding in this picture are explain, recognize, apply and represent. When students complete the progression of the standards, they will not just be able to do math but really understand it.

3. Developing 21st century skills

“Why can’t it just be done the way I learned?” is a question I hear often from parents regarding the CCSS. The fact is, our students aren’t growing up in the same world we did, and we owe it to them to prepare them for today’s society. Our students will likely be doing jobs that haven’t even been created yet!  

So how do we prepare students for those jobs of the future? We teach them 21st-century skills such as problem solving, communication, and digital fluency. A colleague of mine, Rob Kriete, created an awesome visual representation of these skills for parents and teachers. The CCSS for math also include eight math practice standards (link is external) which are habits of mind embedded within the instruction of the content standards. These are not standards that can be checked off a list--like being able to solve an equation--but are skills to be developed across all grade levels.  In these practice standards, students are asked to persevere in solving problems, construct arguments, critique others’ arguments, and use appropriate tools in problem-solving. Being able to do these things will prepare our students for success in college and careers--even the jobs that don’t exist yet.

Like I said before, no set of standards will ever be perfect. But I truly believe the CCSS for math are putting our students on the track for success in the world in which they live. That’s what we all want for our kids, right?

Lindsey Walborn is a high school math teacher in China Grove, NC, who has nine years of classroom experience and is working towards a M.Ed. in Curriculum and Instruction. She has been a math department chair and currently leads a learning community for teachers of Math 3.  Lindsey is also a member of Center for Teaching Quality Collaboratory and works closely with Student Achievement Partners

Math Is Everywhere!

Does this image look familiar? If you have walked the halls of Paine Primary you have passed by this décor. Have you ever thought about the math you see all around? In this picture, do you see four squares that come together to form a new shape? You also see a shape called a rhombus, which is a simple quadrilateral with four sides having the same length. Could this image also be of a tessellation, which consists of one or more geometric shapes with no overlaps or gaps? Yes, it is! Math comes alive as we look around.


Talk to your children or students about the math that you see, no matter where you are. It is critical that children realize math is not an isolated time during the school day. Math is part of every subject and is inside and outside the doors of the classroom all around us.

 

Number Combinations and Dominoes

Having your students sort out the dominoes needed for each of these games is part of their learning, so be sure to let them do the "work" of finding the dominoes they'll be using! For the first level, they'll need to sort dominoes with dots that total one to six. They will then put one domino on each of the petals of their flower. Players take turns rolling one die and then looking for a domino that totals the number they rolled. If they have one, they remove that domino from their flower. Here, the player rolled a three and is removing a 2+1 domino.

If the player has no domino that totals the number, he misses that turn. The first player to remove all of the dominoes from his or her flower is the winner.

Level Two is played the same way, except that this time players will be rolling two dice and will need dominoes that total 2 through 12. Roll, add, and find a domino with the same sum. Here, the player has rolled a two and a six, and is removing a 4+4 domino.

Source:primaryinspiration.blogspot.com

iPad Math Apps That Rock!

10 Frame Fill—Provides children practice with recognizing additive “10 Families” (e.g., 1 and 9, 2 and 8, etc.).





Number Flash–Children practice seeing numbers in terms of the important benchmarks of 5, 10, and 20



Subitize Tree ($0.99 and worth it!) In this app, there is a picture of a large tree with a set of doors.  The doors open up to reveal an object for a short period of time for students to subitize.  Then the doors close and the student has to touch the correct number.

Great visual for decomposing numbers! Thank you, Donna Boucher from http://www.mathcoachscorner.com/

Take A Walk To Be Better At Math: Embodied Cognition Gets Brain Thinking In Sync

This article is very interesting!


May 26, 2015 02:22 PM By Chris Weller     


You might look ridiculous pacing around the restaurant trying to figure out how much each of your friends owes, but new psychology research suggests you’ll get the last laugh.
Thanks to a mechanism in the human brain that likes to pair related, abstract concepts, scientists have found a so-called “congruency effect” in studying how we think. Similar to the infamous Tetris effect, in which extended gameplay can make other parts of your life seem to be nothing but L-shaped blocks and elusive straight pieces, the research shows the brain has a preference for addition and subtraction based on walking left or right.

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Over the last decade, psychologists discovered the interesting fact that doing addition was much easier in an elevator that was going up, and subtraction in an elevator going down. They also found we tend to conceptualize larger numbers better when we’re moving to the right and smaller numbers when moving to the left. In the latest study, a team from the University of Bologna and the Italian National Research Council tested whether walking direction affected people’s ability to add or subtract.
To do this, they recruited 52 people to perform a task. Each participant received a number and was then told they’d be adding to it or subtracting from it later on. The investigators then told them to begin walking and to turn either right or left and begin doing the arithmetic.
After being told a number and which operation to perform, subjects were instructed to walk either right or left. Those who walked right added better and those who walked left subtracted better. Anelli, et al.
The results showed people were far better at adding numbers when they turned right and subtracting numbers when they turned left. “Our finding complements and extends previous results revealing that the direction of body motions can influence not only number magnitude in a number generation task,” the researchers wrote, “but also the more complex process of calculations that leads to a numerical magnitude.”
In other words, moving in accordance with the math problem can help us sort out the problem better than sitting still. And it doesn’t seem to be just walking that gets the job done. Other research has shown the experience of passive movement helps all the same, which means if you need to calculate your expenses for the month, consider driving around the neighborhood and only making right turns. Or if you’re in the middle of a run and can’t remember how far you are from finishing, head left to subtract from your desired distance.
“The present findings confirm the existence of a connection among numbers, space, and motor processes, by showing the emergence of a congruency effect when subtractions and additions were calculated while moving also along a horizontal axis,” the team concluded.
The study isn’t the first to uphold the benefits of walking. A wealth of data suggests the simple act of putting one foot in front of the other can eliminate depressive symptoms, improve mood, lengthen your life, and reduce stress. Which is good news, if what’s stressing you out is math.


Source: Anelli F, Lugli L, Baroni G, Borghi A, Nicoletti R. Walking boosts your performance in making additions and subtractions. Frontiers in Psychology. 2014.


Chris Weller is a Senior Reporter at Medical Daily, where he covers brain health and other fun stuff.