The three methods to use when praising children, as cited in this article, are:

- Praise The Process
- Never Make It A Competition
- Use Observational Language

Wow! Such simple tweaks really make a world of a difference. Most of us (parents and/or teachers) act with good intentions. We want our children/students to be confident, happy, healthy, and we want them to grow. However, perhaps some of the ways in which we THINK we are nurturing our children to be mentally strong are not actually eliciting the results we want. I try to tell myself: don’t just go for the “quick fix;” we want to be in it for the long-term. When motivating others, especially children, it’s tempting to just do what will make them happy *now,* reward them for *now*, dare I say it, bribe them *now*, just get them to do what you want them to do…*NOW*! This may seem like it’s working, but does it create intrinsically motivated, life-long confident and mentally strong people? Not necessarily. I really took the advice in this article to heart, and have started implementing some of the language tweaks the article advises with my own children. As always, I’m also looking forward to tweaking my own teaching starting this fall.

Here is a brief overview of each of the three aforementioned points, and some simple ways that I feel they can be utilized in the mathematics classroom.

*Praise The Process* – Don’t reward or praise based on an outcome, but based on the process. This couldn’t be more true for math, since math *is* a process! “Show your work!” is a phrase often heard in any mathematics classroom. How did your students arrive at their answers? Did students use different strategies? Did students use prerequisite knowledge appropriately? Even if some of the process was incorrect, it is still important to acknowledge the different problem solving strategies students use. During class discussions, praise as many students as possible on their process in arriving at their answers. When students hear you are pleased with various aspects of their problem solving, they may be more confident and willing to try different strategies in the future. You may even get more willing volunteers to participate in sharing how they arrived at their answers to various problems. And please, try to award partial credit as much as possible!

*Never Make It A Competition* – It’s difficult to not compare student to student, but avoiding this will help your students intrinsically feel good about themselves, rather than feeling good about themselves as compared to others. Here is a classic example: a student fails two tests in a row. On the third test, the student earns a 72%. This is a great achievement for this student. However, the student talks to others in the class who all score in the 80’s and 90’s. Compared to the rest of the class, the student did poorly. However, compared to the student’s own historical performance, the student improved so much and actually did great! Write a note on that student’s paper congratulating the student’s improvement. Let the parents know how pleased you are to see the improvement. Offer suggestions as to how the student can build upon the progress. Try to encourage your students to track their own progress throughout the year, and to not compare themselves to others. Most importantly, don’t be the one doing the comparing.

*Use Observational Language* – Provide details to students on what you like about their work. Instead of saying: “nice job!” you can say: “You labeled your diagram really clearly, which helped you to better organize your work” or “you used really efficient steps in solving that equation” or “you did a great job factoring here!” Students will better understand their progress if you provide detailed feedback on their processes, rather than just saying “good” or “great work” or other simple praises. Plus, it shows students that you are really paying attention to their work, which will also make them feel appreciated.

These are just three simple ways in which a teacher (or parent!) can better use praise in order to create more long-term confident children. This author uses the phrase: “mentally strong.” What does it mean to be “mentally strong?” To me, it means someone is confident, un-rattled by bumps in the road, and able to overcome fears. A mentally strong person is not afraid to try something new, and can perform well under pressure. To me, these are qualities I try to elicit in my students, and also in my own two children, every day. I am going to continue to use these strategies, and even though I may not see immediate changes, it is my hope that in the future, those kids with whom I’ve worked, will grow into confident, mentally strong adults. Hopefully those mentally strong adults will continue to pay it forward, as well!

Ask yourself and think about these simple questions: How do you motivate others? How do you praise? How do you foster confidence? How do you think these three strategies would work? How would you feel if someone used these strategies with you? Why would these tweaks make a difference to your students?

Try them, and see for yourself! Good luck!

]]>This is certainly an unprecedented time, to say the least. If you work with children in any capacity, you are definitely facing certain challenges. Parents are trying to fulfill many different roles while at home. Teachers are moving to virtual platforms, whether synchronous or asynchronous, which means learning may look a little different in your home.

In conversations with friends and family, some common concerns keep arising: With less “school time” for our children, how can we be sure that our children are gaining an essential education? How can we foster more educational activities at home? Are my children learning everything they need to learn? With all the societal issues we are facing right now, parents are unfortunately confronted with these additional stresses.

This post is designed for parents (of young children) who are not familiar with teaching math, in order to help ease some of those concerns. As a high school math teacher, but also as the parent of a very young child, I am learning more and more the connections between what I can reinforce at home now, and how it connects to what my son will need to know, believe it or not, when he’s in high school. Building and reinforcing mathematical foundations early in life helps to develop critical thinkers and better problem solvers. This is one of the most important goals of our mathematics classrooms.

This global pandemic will (hopefully) be a small blip in time, and we will return to normal, or a “new normal” I suppose, as soon as we are able. In the meantime, there are simple and fun ways to engage your children with mathematics while staying at home. Some of those opportunities that I’ve noticed while staying at home with my own son are listed below. This “Top 10 List” will hopefully help you brainstorm how you can foster “M.A.T.H. – Math At The Home!”

You are probably already naturally doing some of these activities, but sometimes small changes in how you question your “students” (a.k.a. your children!), can make a big difference in igniting key mathematical concepts. Teachers spend their whole careers honing their craft, and a large component of that craft is questioning. Questioning is a strong pedagogical concept that teachers continue to refine year after year. How you initiate with a question, and then how you build your questioning as you respond to various answers can have a profound way in how kids learn and synthesize information. Keep your questioning in mind when you work with your children!

**Count.**Count all day long. For example, count items in your house, but furthermore, count how many blue books are on your shelf, then count how many red books are on your shelf, count the number of seconds you are washing your hands (hopefully 20!). Ok, that was an easy one. Furthermore, please don’t be afraid to introduce the concept of 0 to a young child! If you have 0 of something, you have none. You can also**.**I see no reason why a young child can’t at least learn how to count by 2’s. But, you should physically show this with…anything in your home! Marbles, blocks, paper clips, whatever you have! When you’ve mastered 2’s, I would say up until 20, try 5’s, and then try 10’s. The National Museum of Mathematics (MoMATH) once recommended a cute book titled: “Sheep Won’t Sleep: Counting by 2s, 5s, and 10s” that my son loves. It is a nice introduction to this concept.

**Abacus and Number Lines.**Take your counting to another level by using an abacus. If you don’t have an abacus in your house, make one! Use pipe-cleaners, straws or string, stretch them between 2 support pieces (wood, a shoe box, etc.), and use beads, or even pieces of paper with a hole punched through to string on each of those lines. It’s simply a tool for counting, and if you make one, well that can count (pun intended) as your “arts and crafts” project of the day! When I search “DIY Abacus” on Pinterest, these are the ideas that appear. They’re great! As far as a number line goes, all you need to do is draw a horizontal line, and list numbers in order from left to right over a certain interval (for young children stick with counting by 1’s). Number lines are certainly used by all math students across all grade levels in a variety of ways.

**Subitizing.**Subitizing is something everyone does without realizing it’s called subitizing. Read this blog post for a nice overview. Subitizing is the ability to recognize the number of a small group of objects without counting. Subitizing helps to develop pattern recognition. It is also a key component in kids learning how to group in elementary school. A great example of subitizing is rolling a die. Whichever side the die lands on, if you can quickly recognize what number that side represents without counting the dots, that’s subitizing. Playing traditional “Double Six Dominoes” is a fun way to emphasize subtilizing, and this game is perfectly suitable for a very young child. When playing the game, have your child announce the number that he/she is working with, in order to reinforce the association between the visual and numeric value. (Also, this set on Amazon is only $6!)

**Arithmetic.**You can put a simple arithmetic-spin on everyday household chores or activities. For example, this morning we made 6 hard-boiled eggs for breakfast. My son helped me peel the eggs. When we peeled 1 egg, I said: “We started with 6 eggs, and we already peeled 1 egg, how many eggs do we have left to peel?” He quickly knew the answer was “5.” Now, I could have kept subtracting 1 each time we peeled an egg, but instead, after the next egg, I said: “We started with 6 eggs, and we already peeled 2 eggs, how many eggs do we have left to peel?” and so forth. Rather than continuing to subtract by 1’s, I wanted to emphasize subtracting different amounts from 6. This is a good example of how parents are probably already doing this at home, but a simple twist in the questioning can elicit deeper learning.

**Algebra and Equations.**I will put Merriam-Webster’s official definition for algebra here: “a generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.” What if we didn’t use letters, and we just used everyday language like “how many?” So, try doing arithmetic, but have your child fill-in a number instead. Let’s use the egg example. This is how I would have asked a question if I wanted my son to do algebra, rather than arithmetic: “If we started with 6 eggs, how many eggs do we have to peel so that we have 4 left?” Guess what…that’s algebra! The “how many eggs” can be replaced by “*x*” and you have the equation 6 –*x*= 4. Building on algebraic concepts, young children can definitely work with equations. For example: “I have 3 blocks in this first tower, and I have 2 blocks in this second tower. How many blocks should I add to my second tower so that each tower has the same number of blocks? The visual of the physical towers helps children clearly see that 1 block is the answer. A very young child doesn’t need to know that this is a word problem that translates to: 2 +*x*= 3, but that is what you are basically doing. This type of concept can be used in a variety of activities with just about anything in your home. Using that type of language is helpful when students learn how to translate word problems into symbols. Word problems are consistently one of the hardest concepts to grasp in school, but introducing this type of language early on may help alleviate some of those struggles in the later years.

**Measuring.**You can tackle measuring in different ways. The other day, my son and I spent close to an hour on this one activity: We measured various items around our home with a tape measurer. We created a table together with 2 columns: “item” and “length.” We then picked four of the items we measured, and created a bar graph to show how long each item was in inches. I made the graph template, and he colored in the bars. He didn’t create the scale for the length, but he counted the numbers as I wrote them! He was then able to answer different questions I asked him by interpreting the graph, such as “which item was the longest?” “Which item was the shortest?” “How long was ____?” and so on. All in this hour, my son practiced the following mathematical skills: counting, measuring, using tools appropriately, transferring information to a table, translating a table into a graph, interpreting a graph, critical thinking. This is just one example of a measuring activity that can be adapted in countless ways! Other ways to measure: don’t use traditional units (i.e. instead of inches, how many sneakers-long is this, or how many crayons-long is that?) or weigh items using a scale. Furthermore, using tools appropriately is a key skill needed and developed year after year in school.

**Units and Conversions through Cooking.**It seems that everyone is cooking more than usual nowadays, and there are endless concepts to learn from cooking. From a math perspective, focus on the numbers in a recipe. Temperatures, quantities and time intervals are all elementary concepts that children can learn and that we can reinforce through cooking. Fractions are apparent in many recipes. “If we need 1/2 cup of milk and 1/3 cup of milk, divided, then how much milk will we need to set out for our recipe?” The answer is 5/6 of a cup of milk, but students in later years of elementary school should be able to find a common denominator and add those fractions. For older kids, work on scaling a recipe. For example, “This recipe serves 8 people, but obviously we’re not hosting anyone, so we need to scale this back to serve 4 people. What should we do with all of our ingredients? Why?” Or, furthermore: “This recipe serves 6 people, but there are 4 people in our house and we want to have enough food for 3 nights. How much should we make?” By the way, you can always add in a “why?” or “how do you know?” to get your child thinking out loud more! Cooking is also an amazing opportunity to practice basic conversions, such as cups, ounces, quarts, etc.

**Patterns.**Patterns are everywhere! Take colored blocks and create a pattern. Have your child tell you what should come next in the pattern. You can do this with coloring also, and your child can practice his/her penmanship. Aside from colors, your child can create patterns with just about anything! Playing cards, different sized objects, different types of books – the possibilities are endless. Creating patterns offers a nice opportunity to practice sorting. Have your kids sort items into piles, and use the piles to more easily and efficiently create the patterns. Patterning is a wonderful skill and a fun way to engage in problem solving and creativity. As kids move through their math careers in school, they learn a lot about functions and sequences. A major component of functions, particularly linear functions at the end of middle school/beginning of high school is recognizing patterns in tables. This concept evolves to arithmetic and geometric sequences in the later years of high school where students work with both explicit and recursive formulas to find specific terms in a sequence.

**Shapes.**Keep emphasizing different shapes whenever and wherever you can find them! Don’t be afraid to teach young children the proper names for shapes and solid figures (a.k.a. 3-dimensional shapes). Children should know “diamond” but you can also teach “rhombus.” For solid figures, a typical box is a rectangular prism, a ball is a sphere etc. Click here for a basic overview of solid figures. A very experienced secondary math teacher and administrator once told me years ago that the more often young children play with blocks, the better they can understand volume and surface area of solid figures when studying geometry in high school. Geometry students need to understand 3-dimensional solid figures when represented on a 2-dimensional flat piece of paper, and being able to visualize the solid figure can help in synthesizing these more complex geometrical relationships. It’s something I see many students struggle with. While we’re on the subject of high school geometry, many teachers use “nets” to teach surface area. Geogebra is a wonderful interactive website, and here is one of their activities on nets. The best real-world example of a net would be to take a traditional box (rectangular prism!) and cut it so that it can lay perfectly flat. What you will find is 3 pairs of congruent (simply put, exactly the same size and shape) rectangles. A cool way to work with nets would be to work with magnetic tiles/blocks. Create a solid figure, like a cube or a pyramid, and then take it apart and lay out all the pieces you used. Some questions to ask: “What shapes did you use to make your pyramid?” “Are all the triangle sides that you used the same size and shape?” When your child answers yes, you can introduce a new vocabulary word you now know: congruent!

**Symmetry, WODB and Example/Non-Example.**There are some other fun games and activities to play with things lying around your home, but that emphasize critical thinking and problem solving. Some examples are Symmetry, WODB and Example/Non-Example. Symmetry is a word young children can definitely learn. Introduce it in its most simple definition: “the same on each side.” Obviously, as children get older, this definition will become more sophisticated, but you can teach this concept at young ages, plus it’s a great vocabulary word. Look for items in your home that have symmetry. Maybe you have a dresser, and there are three drawers vertically stacked on each side. Maybe you have a four burner stove, and there are two burners laid out horizontally on each side. Have your children examine letters (or practice writing them!) and discover which letters have horizontal symmetry and which letters have vertical symmetry (i.e. “T” and “V” have vertical symmetry but not horizontal symmetry. “O” and “H” have both!). Not only did you explore symmetry, but you inadvertently taught your kids the concept of vertical and horizontal! I wrote a blog post on WODB that you can read here. “WODB” stands for “which one doesn’t belong.” Take 4 things, present them to your child, and ask: “Which one doesn’t belong? Why?” You can do this in countless ways, and it’s fun to find multiple answers for each problem set. For example: a rectangle, a square, a diamond (rhombus!) and a triangle. A triangle doesn’t belong because it has three sides, while the other shapes have four sides. Example/Non-Example is a simple game that can help build critical thinking skills. An example of a bird is a penguin. A non-example of a bird is a cow. An example of a three-digit number is 142. A non-example of a three-digit number is 23. With these games, it might not seem like you’re doing math, since you’re not calculating anything, but trust me, the critical thinking and problem solving needed to complete these games will definitely come in handy later on, both in and out of the classroom.

11. **BONUS! Time, Money and Phone Numbers.** These are three concepts and skills that are gradually becoming less prevalent as technology continues to evolve. Digital time replaces analog clocks. Credit cards and digital pay services replace physical money. Cell phones and contacts/favorites replace memorizing phone numbers. This generation may not naturally learn these skills well in their every day world, simply because they are not used as often. So, take the time now to teach them to your kids! Use play or real money to teach the names of different coins/bills, and how many coins/bills’ values equal a larger coin/bill’s value. Paper and coin money is also a great tool for arithmetic and algebra. If you don’t have a play or analog clock at home, draw a picture of one! When I search “analog clock craft” on Pinterest, these are the ideas that appear. If you still have a phone other than a cell phone in your home, use it to teach important phone numbers to you kids! Your own phone numbers, grandparents’ phone numbers, or even 9-1-1 are great first phone numbers to memorize! Click here for a simple way to teach phone numbers using paper plates.

So, there you have it. Just 10 (and a bonus!) examples of some simple ways to institute “M.A.T.H.” for your younger children while staying at home. The best piece of advice I can offer is to not stress out too much about what your kids are missing, but to try to focus on what your kids are gaining. They have the unique opportunity to learn from you, so go for it! Every day in my classroom, my students ask me the inevitable question: “When are we ever going to use this in real life?” It’s difficult for them to understand that they had been using these skills all along in their formative years. Hopefully years from now, when you are talking about this incredible time in our history with your children, you’ll have the stories to tell them all about how they did “M.A.T.H.” And better yet, that it was fun!

If you have other ideas to add, please share and comment below! It would be wonderful to build an on-going list of “M.A.T.H.” for all parents.

Stay healthy and safe!

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!

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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.

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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.

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