In class, I have incorporated writing in a few small activities. In the beginning of the school year, I asked each student to write down goals for math class for the upcoming year.

Some responses included:

“To get better at math.”

“I want to not fail and work harder.”

“Have fun and enjoy math! ”

Responses tended to be shorter, and more phrase-like, especially from my Freshmen classes. Students wrote these responses on Post-It notes, and we displayed them on large posters in the room. This way, students are always able to refer back to their original goals. It holds a certain accountability when they can see their own words written in their own handwriting.

Phrases, however, aren’t enough. I want students to gain a level of sophistication in how they express themselves in math class (appropriate for each individual, of course). So, I have begun to ask more thought-provoking questions about our work throughout the year, asking students to write down their answers using complete sentences. Furthermore, I have tried to make my questions more specific, rather than vague. I have come to realize that specific questions elicit more specific answers, while vaguer questions elicit more vague answers.

Most recently, I asked my Algebra students: “If you check your solution to a system of linear equations, why does the solution work in both equations?” Students know to substitute their coordinate point in each equation to see if it “works,” but I really wanted them to understand *why*. It also helps bridge the gap between the graphical representation and the algebraic representation of a system of linear equations.

Here are some responses:

“The x value and the y value work in both equations because they are the same in both equations.”

“Because there are three different methods of doing this type of question, and you need to check your work to see if you get this equation/problem right.”

“The solution is the point of intersection of the two lines.”

“It is the same equation written differently.”

“It’s linear, so they have the same slope.”

“Both equations share the same x value and y value.”

“They both have a point in which they cross.”

While some responses are a bit more reasonable than others, I was pleased to see students using decent vocabulary. They were also writing slightly more complex sentences than their phrases from the beginning of the year. It’s clear they have some sense of what the answer means to my question, even if their answers need more fine-tuning.

In my Algebra 2 class, I asked the following question: “Which should always have a higher value: sine or cosecant of the same angle? Why?”

Here are some responses:

“Cosecant, because the hypotenuse is the longest side of the triangle and for cosecant the hypotenuse is on the top.”

“The cosecant should be higher because it is the flipped of sine.”

“Cosecant has to be higher, because the hypotenuse is the longest side of the triangle.”

As we can see, they were trying to express the concept that cosecant is the reciprocal of sine, which brings the hypotenuse, the longest side of the right triangle, to the numerator. They used some good vocabulary, while other vocabulary could be expanded upon (i.e. use “reciprocal” instead of “flipped,” or “numerator” instead of “the top”), but they were definitely trying to describe the differences between sine and cosecant.

As the Math Research director at our school, I advise students throughout the year in researching a topic in advanced mathematics. These students also write a 10-15 page research paper and prepare a presentation for a local competition involving dozens of school districts and over 400 students. This is no easy task. These students struggle to begin their papers, because they have found that they have never written an essay about math before. It also takes some practice interweaving equations and mathematical concepts throughout the paper, without sounding like a textbook. I have worked, and continue to work, to help my students use detailed and clear explanations, while using proper vocabulary to describe the mathematics that they are researching.

The trend between my classes and my math research students is that students feel more comfortable, and are more adept at, writing about math in a straight-forward, fact generating way, rather than truly analyzing the concepts. We could all use a little more practice in this area. Students can definitely learn to write more analytically about mathematics, and teachers can also learn to assign specific writing prompts in order to elicit detailed, more complex responses. I hope to continue to practice helping students become better, more analytical writers in the field of mathematics for years to come.

]]>So, if our world is saturated with pictures, then where are all the words?

That leads me to another question: are we writing less? On the one hand, we email, text, and comment so often that it seems that we are writing more and talking/using pictures less. But, on the other hand, we are using images so often that it seems that we are using pictures more, and writing/talking less. It’s a little confusing! The bottom line is this – writing skills may evolve over time, but they aren’t going away. So, we need to practice writing in as many facets of our daily lives as possible.

As a math teacher, I do think about ways in which students can practice writing. Students traditionally don’t think of math class as a place for writing. However, I do believe that their perception can change and evolve if we give them the proper tools and support to practice their writing. We all know that “showing work” is an important part of mathematics. We expect our students to guide us through their thought processes by writing down each step they take to solve a problem. That way, we can “see” how they are thinking. We have also come to expect students to verbally explain their reasoning. Whether it be through answering questions orally in class, or through other activities such as gallery walks, peer to peer activities, or peer grading. Students really do tend to typically have some opportunities in class to express themselves verbally.

However, what about explaining their reasoning with written words? Often times we attach to our assessment questions an extra “explain” or “explain why” or “explain your reasoning.” What does this mean to our students? Are these directives too vague? Perhaps, with some more pointed and specific directives, our students can practice writing about mathematics and practice explaining their reasoning effectively. This is great foundation work for future careers and their every day lives. There is a high demand in both our professional and personal lives to write, especially through the following channels: emails, texts, social media posts, profiles. Students need to be able to use words to express themselves in a variety of ways. Since there are so many different means and mediums with which we communicate, students need to be prepared to tackle these tasks in their adult lives. The time to start practicing is now, and what better venue than in math class.

In the near future, I will aim to follow-up to this post by explaining some specific writing strategies I have tried, and want to try. As the school year is fast approaching, I’m looking forward to learning and growing with my students, and encouraging them to explain their thinking through the written word.

]]>I couldn’t imagine sacrificing teaching time with my teens, and I also couldn’t imagine sacrificing daytime fun with my son, so luckily, I have been fortunate to have the opportunity to teach part-time while I navigate this new world of parenthood.

This has afforded me an opportunity to make some interesting connections between my existing role as a teacher, and my new role as a mom. My day is split between two different environments with two very different age-groups, however, much of my day is actually spent doing the same thing. Well, not exactly the same, but my routines and daily activity are suspiciously analogous to one another.

It’s like I live 2 lives, but they are really different, yet similar, but different, yet still so similar!

Here are 5 of my many observations on the connections between teaching and parenting:

**I’m A Super-Model!** – I find I’m constantly modeling behavior that I want to elicit from both my son and my students. I show my son how to play with toys, how to eat, how to make noises, and he is always up for the task of doing as I am doing. It’s such a thrill to praise him when he succeeds, and to see him grinning from ear to ear with enthusiasm and self-worth. It’s the same in my classroom. Not only am I modeling mathematical reasoning, organization and critical thinking, but I model how to treat others with respect, and how to stay calm and focused in the face of adversity. It’s such a thrill to praise my students when they succeed, and to see them grinning from ear to ear with enthusiasm and self-worth. Hmm, where have I heard that before?

**Smile At The World, And The World Smiles Back** – My son’s Great-Grandparents gave him this excellent piece of advice months ago, and I couldn’t agree more. Creating a happy and calm environment, both at home and in the classroom, requires both a deep-breath and a smile. When I see my son, I smile, and he knows I’m happy to be with him. When I see my students, I smile, and they know I’m happy to be with them. Even if I’m not in the mood, I make it seem like I am, because I know that smiles can really go a long way in making someone’s day brighter and more positive.

**Don’t Take It Personally – **Sometimes, it’s just one of those things. No matter what you do or what you say…the baby is crying, or your students are annoyed, or your kids are distracted by something completely unrelated to you. It is what it is. I always tell myself: don’t take it personally! I just keep doing what I need to be doing in order to make the most of my time with my kids. Maybe I won’t get to teach my entire lesson this period. Perhaps I won’t get to read the book I picked out for this moment. It’s ok, because “after all, tomorrow is another day” (yes, I just quoted *Gone With The Wind*!)

**Go With Your Gut – **If you ask 50 teachers how to teach a particular topic, you could get 50 different answers. If you ask 50 moms how to handle a particular situation, you could get 50 different answers. They’re not necessarily right or wrong, but they are different! Students, babies, kids – they are all people. They are living, breathing, ever-evolving human beings. For either role, it’s an amazing thing to have a network of peers to reach out to, whether it be through family, friends, social media or other like-minded groups. And it’s a great method to brainstorm for different ideas, routines, products, and how to solve a particular problem. However, I really try to always go with my gut instinct. I am the mom/I am the teacher. This is my son/these are my students. I know what’s best. What worked for one, may not work for another. What works one day may not work the next day. Whenever I’ve gone with my gut, both as a mom and as a teacher, I’ve always been pleased with the result.

**When In Doubt, Sing! – **I sing ALL DAY LONG. One would think I was a choral teacher. Seriously! “Where do you come up with this stuff?” everyone asks me. Honestly, I just sing what comes to mind. And it sticks. My students remember steps/topics/facts through my wacky songs. My son remembers songs that I sing to him, as well. Plus it’s fun. And if you’re not having fun doing what you’re doing, well, come on, wouldn’t you rather have fun then not have fun?!

So there you have it. Some connections between teaching and parenting. Two “jobs” where constant learning and adaptation are paramount, and where knowing your audience is crucial. I guess, in sum, you could say that it’s my gut feeling to model good behavior by smiling and singing a song. And if things don’t necessarily go according to plan, I won’t take it personally!

]]>

This generation loves information more than they realize. They are enamored with “Googling,” and can’t wait to look something up, even when they probably can, given some time, think about a response for themselves first. This “instant access” to information is truly amazing, and has many benefits, including: being able to find history facts, movie times, weather/traffic updates, or looking up a rogue “factoid” just for fun, and very quickly.

However, does simple factual recall create better learners? Instantaneous gratification is certainly a factor in hindering learning, at least from what I am witnessing in my classroom. Could this be because students aren’t used to thinking things through without looking up an answer on the spot? I’m concerned about our students’ memories, and their attitudes for learning without using the Internet or their mobile devices for help. For example, after five minutes of discussing a topic, they can be quick to claim: “I don’t get it!” or “I didn’t know what to do” and want to give up because they don’t know the correct answer right away. I encourage them in this way: “well, that makes sense. We’ve only been discussing this for five minutes. Let it sink in a bit. Think about it some more. It might take a few days, and that’s ok!” I want them to know that it’s perfectly reasonable to not know the answer right away. The old adage “patience is a virtue” is true, and I want my students to give themselves time and space to learn, rather than rush to answers that, without critical thinking, can be meaningless and quickly forgotten.

The below quote from the NPR article perfectly sums-up the concern I have for this instant access to information:

“A 2011 study in the journal *Science* showed that when people know they have future access to information, they tend to have a better memory of how and where to find the information — instead of recalling the information itself. That phenomenon is similar to not remembering your friend’s birthday because you know you can find it on Facebook. When we know that we can access this information whenever we want, we are not motivated to remember it.”

To combat this resistance to taking time to learn, resourcefulness is important in my classroom. While students are encouraged to look to their past notes for information (information that they curated themselves, rather than from the Internet!), we mostly spend time commenting on each other’s claims and responses, and also ask each other for advice on how to solve problems. We discuss different methods of remembering facts, and other connections they can each make across our own mathematical units, different branches of mathematics, and other subjects in order to better recall information and synthesize different topics. Usually, before I even begin a topic, I simply ask the class what they know. In due time, students are brainstorming their preexisting knowledge of the topic, which usually puts everyone at ease, since they now have assurance that they know *something*, even before we start. Learning is happening, and instead of turning towards “the screen” for answers, we turn towards ourselves.

So, the Internet and mobile devices are truly amazing for a variety of reasons, but I do believe we can live without them once in awhile. Let’s try to think for ourselves, make our own connections, and have conversations about topics, rather than look to our screens for all the answers. And if not very often, at least for 40 minutes a day in math class!

]]>But, teenagers have very little experience with managing money. Some may have a job, others may have an allowance, but very few actually know what happens when you earn a paycheck and need to save money to pay for your every day expenses.

In my business math class, we spent time talking about payrolls and budgets. We discussed the different ways one can be paid, such as salary, hourly, and commission, and of course the deductions that occur on your paycheck, such as Federal Taxes, Medicare, and Social Security. The students were astonished as to how much money truly gets withheld from your paycheck!

We then moved on to talk about budgeting your money, and the typical expenses you pay throughout the year, such as utilities, rent or mortgage, entertainment, insurance, food, transportation, etc. The kids commentated on “how hard it seems to have enough money to pay for everything.”

So we discussed the importance of keeping track of your money by being diligent and organized in recording your spending. Exercising 21st Century Skills and digital literacy, we used Google Sheets and Microsoft Excel to create a monthly budget spreadsheet. Students learned how to create formulas within the software, and how to highlight, bold, and underline to make the spreadsheet easy to read. For some students, it was their first experience using Sheets or Excel, and many commented on how “amazing” it was to see the software do so many calculations, particularly in using the formulas function.

For the actual project, students picked a job and salary, and then used actual NYS Withholding Tables to determine their taxes withheld. They needed to use proportions to determine the amount for only one month. They also calculated the Social Security and Medicare amounts using percentages. Students then chose some expenses to include in their budget, and estimated how much those expenses would be for the month. Finally, students used Google Docs to write a reflection on what they learned from their experience creating this budget. They uploaded both the spreadsheet and reflection to Google Classroom, where I read their submissions, and replied with private comments and grades for their work. All of this was graded using a detailed rubric the students had access to from the onset of the project.

All in all, this was a great project for the students. Not only did they gain experience in working with budgets, but they exercised 21st Century Skills and Standards of Mathematical Practices. In particular, the kids used the 21st Century Skills of: Communicating, Analytical Thinking, Problem Solving, Finding and Evaluating Information, Creating and Innovating, and the Standards of Mathematical Practices of: Constructing Viable Arguments, Modeling Using Mathematics, Using Appropriate Tools Strategically, and Attending to Precision. In the future, I may have students create a real budget for their current lives. Perhaps the students would feel even more connected to the project, and they could even continue to use their budget spreadsheets through the year! Either way, the hands-on and practical aspect of this project proves to be worthwhile in forging business and math topics in this particular class.

]]>

I commend Strachan for composing such an approachable and light-hearted anthology. Each topic is at most a few pages long, so it’s easy to read a section or two at a time without getting overwhelmed. She includes real stories from her teaching days, including some of the student reactions that make her stories come to life. Strachan is also clear in her mathematical explanations, which makes this book easy to follow.

A Slice of Pi will grace my bookshelf both in my office and in my home for years to come.

]]>I have previously worked in a 1:1 iPad environment, and used iTunes U in its infancy to disseminate handouts and class notes, post information about assessments and share videos and other resources with my students related to the curricula. I got so “into it” that an Apple iTunes U manager picked up my work, and invited me to join a small cohort of teachers who were considered first-movers in the iTunes U community. We collaborated online and shared ideas about teaching with iTunes U. Colleagues I met through that group continue to be inspirational in their uses of educational technology.

Now, working with 1:1 laptops, I no longer use iTunes U, but have shifted to begin using Google Classroom. I am so impressed so far, that I am working towards converting to completely “GAFE” (Google Apps for Education). Since my school uses Google products for email, calendars, and storage (Drive), it is proving to be a seamless transition. Currently, I created contact groups of my students and invited them to their specific section’s Classroom page. Course descriptions and outlines for my courses are already posted, as well as my first homework assignment with a due date! I recently read that Google Classroom will soon utilize a calendar to organize all assignments, which is exciting, as I already use Google Calendar on my Site so students can keep track of homework assignments.

Assignments and showcasing work will definitely get an upgrade in my courses this year. A cool feature is the ability to review and grade work through Google Classroom, as students are able to upload Docs, Spreadsheets or Slides from their Drive right into an assignment in Classroom. This presents an opportunity to integrate more literacy and writing in the math classroom, because I can ask students to submit write-ups or presentations, or even have my Business Math class submit spreadsheets. Google Photos is the newest Google feature to impress me! A longtime Picasa Web and Google+ user, transitioning to Google Photos was easy. Photos are automatically saved and categorized, so I hope to use this feature at some point during the year, as well.

With the help of GAFE, I am looking forward to a wonderful new school year full of successes, learning opportunities, technology, and fun. I also welcome any suggestions, tips and tricks in using these awesome tools.

Have a great year, everyone!

]]>The first tip is particularly striking. It’s titled: “Don’t steal the struggle” and encourages teachers to take a step back while kids are thinking and working through tough material. The article confirms that “[i]t can be uncomfortable to watch kids struggle to figure out an answer, but they need time and silence to work through it,” and I completely agree. It can be stressful for a teacher to let these things happen in the classroom, when we as teachers are usually so quick to correct, to assess, and to move the lesson along in our allotted 40ish minutes. However, when teachers take a step back, and let the students work through the struggle, truly impactful learning can take place.

In my math classes, I expect students to struggle, to make mistakes and to spend time trying different strategies in order to effectively solve problems. To me, it’s OK if students don’t get the correct answer quickly, because it provides an opportunity for students to learn from their own mistakes. Rather than automatically give the right answer to struggling students, I ask questions such as: “How did you come up with that answer?” or “Can you prove what you just said to be true? How?” or “Why was your strategy effective or not effective in solving the problem?” Asking questions such as these to kids struggling in class and/or kids who simply answer “I don’t know” is a technique I have adapted called “No Opt Out” from Doug Lemov’s *Teach Like A Champion. *It pushes students to “not opt out” by encouraging students to keep going, to embrace the struggle, and to gain confidence in being OK with making mistakes, ultimately fixing their mistakes and improving skills. In my classroom, I push students to not only work through their mistakes, but to learn how to also become more resourceful. This can be done by encouraging students to look through their class notes, to take a quick search online, or to ask a friend for help. Furthermore, students communicate with each other in my classroom, offering suggestions for how they can each change in order to solve a problem more efficiently and effectively.

The ultimate goal of emphasizing this self-assessment and resourcefulness is two-fold. Firstly, students should be able to think through a problem on their own so that when they are faced with struggling with a tough problem on an assessment, they will be able to work their way through that problem on their own, without any help. They should be able to come up with different options and strategies to solve the problem, and also be able to assess their own work when “double-checking” their answers so that they may find and self-correct mistakes. Secondly, this concept of being resourceful without a teacher helping the student through a problem will hopefully transfer into kids’ adult lives, when they will ultimately be faced with various problems they have to solve, without being given the answers.

If one of the main goals of math class is for kids to learn how to solve problems, then let’s take this idea of solving problems to the next level. As teachers, let’s “talk less” in order to help our students exercise self-starting and self-assessing techniques. By “not stealing the struggle,” we can help prepare the next generation of leaders, innovators and problem solvers to tackle problems head-on, and work through the struggle on their own.

]]>Yet still, it is always important to find balance in one’s life, and that balance includes a healthy mix of spending time with family and friends, engaging in hobbies (such as blogging!), and working hard and having fun at work. For me, the “fun” is not only being with my students in class each day, but through my involvement with extracurricular activities. Despite the whirlwind of the end of the school year, I continue to participate in extracurricular activities because that’s a major part of why I love my job: working with and being with teenagers. This spring proves to be as busy as ever. Advising our Freshmen class during our annual spirit competition at school took lots of patience and energy. After countless hours of preparation and practice, my math research scholars competed in their last round of competition, winning a variety of medals to close out the season. Our girls’ varsity softball team, of which I am one of two coaches, continues to play extremely well, and we are currently in second place in our division. With all this glory comes time, patience, energy and attention, and of course, these things are not taken out of my regular school day, but my extra free time. In fact, that’s probably how the term “extracurricular activities” earned the prefix “extra.”

But to me, these activities aren’t “extra” at all. In fact, they are a natural way to continue to do what I love. This might not sound like much balance to someone, since it sounds like “all work,” but much of this work is extremely rewarding. Getting to know your students out of the classroom can be an eye-opening experience. You learn things about others, and learn a lot about yourself: how to manage, how to work with a team, and how to advise students outside of your content area. When you see your students succeed in the classroom by performing well on a particular task or assessment, you feel gratified and accomplished. The same can be said about working with students in other areas. Coaching kids through each inning and offering advice on giving presentations does help kids be successful. It’s a way that I try to make an impact on individual student lives, other than through the typical day-to-day interactions in the classroom and during extra help time.

So, the moral of the story is that life gets busy and challenging, and at the end of the year, we teachers can lose sight on what matters most: helping kids. Try not to let the end of year stresses get you down, because you only have a few weeks left to still make a difference in this school year. Your time is limited, but making the most of it will prove to be most rewarding, and of course, fun!

Am I eager and excited to move on to summer for that much deserved rest and relaxation? Of course! But, that rest and relaxation doesn’t come without my need to continue to do what I love, because I get to continue on to an amazing “non”-extracurricular: to work with teenagers, to advise, to coach, and to teach…while at sleep-a-way camp!

]]>Thanks to the following people, my classes were able to face this challenge:

All of my amazing PLN at #MTBoS, Christopher Danielson (@Trianglemancsd), Mary Bourassa (@MaryBourassa), Alex Overwijk (@AlexOverwijk), Andrew Gael (bkdidact) and @WODBMath, as well as these sites and blog posts: WODB Website, Steve Wyborney’s Blog Post, Alex Overwijk’s Blog Post Part 1 , Alex Overwijk’s Blog Post Part 2 , and Alex Overwijk’s Blog Post Part 3.

WODB seemed like a great activity to finally implement on a day that was sandwiched between a test day, and the start of a week-long vacation. I had seen the concept floating around Twitter and the Blogosphere, and really wanted to have an opportunity to try it in my own classroom. Given one period only, I introduced the concept to each class, we sang the jingle together (check out the title of this post for a hint!), and as a whole class, we practiced on a sample foursome card: 2, 3, 9, 11. We were able to quickly ascertain that 2 doesn’t belong because it’s the only even number, 9 doesn’t belong because it’s the only composite number (as well as the only perfect square), and 11 doesn’t belong because it’s the only 2-digit number.

Once everyone got the hang of the activity, my students worked in partners, picked one WODB card at a time, and worked together to come up with *all* the possible ways one of the four things didn’t belong. Some teams came up with a couple of reasons for each foursome card, while others came up with closer to ten or twelve reasons! I allowed teams to choose more than one foursome card so they could work with different types of pictures: numbers, graphs, shapes, or other graphics. There were a few copies of each foursome card, and it was fun to see the different types of reasons each team developed. The “winner” of the challenge was the team who was able to come up with the most number of valid reasons for one foursome card. What constituted validity? At the end of the period, each team had to present their findings to the rest of the class using details, mathematical reasoning, and proper vocabulary, and as a whole class, we decided if the reason was valid. We kept a tally on the whiteboard to keep track!

In addition to all the fun they were having playing the “game,” my students utilized many skills in order to achieve their goal. My students exercised: creativity, communication, team-work, reasoning and sense-making, categorizing, comparing and contrasting, organization, presentation skills, and out-of-the-box thinking. We touched upon each of the Standards for Mathematical Practice, with an emphasis on #2, #3, #7 and #8:

- CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
**CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.****CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.**- CCSS.MATH.PRACTICE.MP4 Model with mathematics.
- CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
- CCSS.MATH.PRACTICE.MP6 Attend to precision.
**CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.****CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.**

Some pictures of some of the teams’ final explanations:

With more time, I would have had teams develop their own WODB foursome cards, and circulated them around the room so teams could practice on each other’s homemade cards. This could be a great activity to revisit in the future, now that my students are exposed to the idea of WODB. It can be used with any topic, at any grade or ability level, and in any subject area, and it exercises a host of excellent skill-sets that benefit all students.

]]>