I’ve always thought language and math skills go hand-in-hand. After all, without strong language skills, solving word problems (and sometimes even understanding directions) is rather difficult.
Plus, language lends itself to logical reasoning. But, I wondered what effect knowing two languages might have on learning mathematics. Currently, the conclusion as to whether it’s helpful or not is still up in the air, but I did find some interesting ways bilingual students and adults use their skills in math. Potential Brain Benefits In such a diverse society, I can’t help but feel that being bilingual gives students an extra edge in life and helps them connect with a wider variety of other students. But, there are also studies that show the brain itself benefits from knowing two languages. One benefit I zeroed in on was improved attention. When bilingual kids and adults switch between languages, they also enhance their executive function skill set. In layman’s terms, they’re able to stay more focused and switch tasks easier without losing their train of thought. This also means they may be able to better switch between different mathematical concepts too. Language Does Matter One in five kids in the United States speak two languages. However, this doesn’t mean they’re as great at math in both languages. Studies show varying results in this area. For instance, I discovered a study that disproved the original theory that students learn math better when it’s taught in the first language they learned. The study was actually performed with teachers, but it showed that the teachers responded almost equally in both languages. They answered slightly faster, though, when the problems were in the language they taught in, not necessarily their first language. So, my belief from all this is students learn math equally in both languages. However, they may work through problems faster and potentially grasp concepts better when math is taught in the language they use most. Overall, there’s little evidence that being bilingual has any real impact on learning mathematics. But, I say if a child is able to learn the intricacies of two languages, they just might be able to better understand a third language – math. 
0 Comments
Teaching Problem Solving Strategies
During my second year of teaching (in the early 90s), I was teaching 5th grade, and our state math testing began to include a greater focus on problem solving and writing in math. Over the next several years, the other math teachers and I used standard sentence starters to help math students practice explaining their problem solving process. These were starters like: “In this problem, I need to….” “From the problem, I know….” “I already know…” “To solve the problem, I will…” “I know my answer is correct because…” By using these sentence starters, students ended up with several paragraphs (some short, some long) to explain how they approached and solved the math problem, AND how they knew they were correct. Sometimes this process took quite a long time, but it was helpful, because it made many students slow down and think a bit more about what they were doing mathematically. They took a little more time to analyze the problem (rather than picking out the numbers and guessing at an operation!). I was teaching 5th grade in elementary school at this time, and we had a full hour for math every day. So, fitting in problem solving practice a few times a week was pretty easy, after students understood the process. I really liked spending the time on these types of math problems, because they often led to discussion of other math concepts, and they reinforced concepts already learned. I used math problems from a publication that focused on various strategies, like Guess and Check, Work Backwards, Draw a Picture, Use Logical Reasoning, Create a Table, Look for a Pattern, Make an Organized List. I LOVED these…I really did (do)! And the students I taught during those years became very good problem solvers. Teaching Problem Solving in Middle School Math When I moved to 6th grade math in middle school, I tried to keep teaching these strategies, but our math periods are only 44 minutes. I tried to use the problem solving as warm-ups some days, but it would often take 30 minutes or more, especially if we got into a good discussion, leaving little time for a lesson. I found that spending too many class periods using the problem solving ended up putting me too far behind in the curriculum (though I'd argue that my students became better thinkers:-), so I had to make some alterations. I liked the format of the sentence starters, but the biggest time-consumer was the writing part. We had to decrease it. Instead of writing so much, we started to: * highlight/underline the question in the problem * shorten up the writing to bullet points * highlight/underline the important information in the problem 
Problem Solving Steps
Now, when I teach these problem solving strategies, our steps are: Find Out, Choose a Strategy, Solve, and Check Your Answer. Find Out When they Find Out, students identify what they need to know to solve the problem. They underline the question the problem is asking them to answer and highlight the important information in the problem. They shouldn’t attempt to highlight anything until they’ve identified what question they are answering – only then can they decide what is important to that question. In this step, they also identify their own background knowledge about the concepts in that particular math problem. Choose a Strategy This step requires students to think about what strategy will work well with the question they’ve been asked. Sometimes this is tough, so I give them some suggestions for when to use these particular strategies: Make an Organized List: when there are many possible answers/combinations; or when making a list may help identify a pattern. Guess and Check: when you can make an educated guess and then use an incorrect guess to help you decide if the next guess should be higher or lower. This is often used when you’re looking for 2 unknown numbers that meet certain requirements. Work Backwards: when you have the answer to a problem or situation, but the “starting” number is missing. Make a Table: when data needs to be organized; with ratios (ratio tables). Draw a Picture or Diagram: when using the coordinate plane; with directional questions; with shape-related questions (area, perimeter, surface area, volume); or when it’s just hard to picture in your mind. Find a Pattern: when numbers in a problem continue to increase, decrease or both. Write an Equation: when the missing number(s) can be expressed in terms of the same variable; when the information can be used in a known formula (like area, perimeter, surface area, volume, percent). Use Logical Reasoning: when a “yes” for one answer means “no” for another; the process of elimination can be used. Solve Students use their chosen strategy to find the solution. Check Your Answer I've found that many students think "check your answer" means to make sure they have an answer (especially when taking a test), so practice several strategies for checking: * Reread the question; make sure your solution answers the question. * Redo the math problem and see if you get the same answer. * Check with a different method, if possible. * If you used an equation, substitute your answer into the equation. * Ask - does your answer make sense/is it reasonable?
Teaching the Strategies
I teach problem solving strategies as a unit, teaching and practicing each one, and then incorporate the strategies and our 4-step process as students approach problems throughout the year. They keep reference sheets in their binders, so they can quickly refer to the steps and strategies. Some strategies are used more frequently than others (Draw a Picture, Write an Equation, Make a Table), but it's important to know that others are possible. During the unit, I like to show them the same problem, solved with different strategies. For example, I often find that a 'Guess and Check' problem can be solved algebraically, so we’ll do the guessing and checking together first, and then we’ll talk about an algebraic equation - some students can follow the line of thinking well, and will try it on their own the next time; for others, the examples are exposure, and they’ll need to see several more examples before they give it a try. Doodle Notes This year, I'm trying something new - I created a set of Doodle Notes to use during our unit. The first page is a summary of the steps and possible strategies. Then I created a separate page for each strategy, with a problem to work through, as well as an independent practice page for each. I also created a blank template, so I can create problem solving homework for students throughout the year, using the same format. I'm hoping that using the Doodle Notes format will make the problem solving strategies a little more fun, interesting, and easy to remember. To check out the Problem Solving Doodle Notes, click the link or the image! 
To Read Next:
Teaching Middle School Math
Teaching math isn’t easy, but with the right resources, it’s much easier to connect with your students and improve your teaching practices. There are SO many options and resources out there for us to choose from. Sometimes, depending on the topic, there's so much available that it can be overwhelming.....while for other topics, it's challenging to find anything that fits our exact needs. For this post, I've chosen some sites/resources that could help you in your math planning. 1. Lesson Plans (obviously!) Sometimes it’s hard to come up with a great lesson plan....you just get stuck. When I started looking online, I was surprised to find so many great lesson plans for all grades and subjects, including math. For me, it’s a great way to get ideas, even if I don’t follow the exact plan. I love sites like PBS Learning Media and TeachingMath.org, which have a variety of lesson plans and activities to help inspire us. 2. Teaching Groups/Collaboration There are many groups of teachers from different parts of the world who have found each other through social media and have created or joined Facebook groups. These groups share teaching tips, discuss teaching methods and philosophies, and offer support and advice. One group I'm part of is called Let's Talk Teaching Teens - this one is for teachers of middle and high school teachers. It's exciting to share with, learn from, and help teachers around the world! 3. Games, Puzzles and More My favorite resource for math teachers is actually a bunch of different resources. I’m talking about activities, games and puzzles to keep students engaged. A few great places to start include:
4. Books! I love reading books to find ideas and improve my teaching, and there are a couple that I think are absolute must-haves. These are by Jo Boaler; I've read others that are good, but I think hers are amazing: 5. Pinterest Boards I'm sure you're already all over Pinterest, but just in case you're not - I can’t tell you how many great resources I’ve found on there. Entering search terms like “math” or “teaching” or specific topics like “equivalent expressions” or “dividing decimals” brings up numerous pins and boards. Fill up your own boards with related resources so you have a place to turn when you're in need of a quick idea. From teaching tips to games, there’s a little of everything. When you’re armed with the right resources as a math teacher, it's so much easier to help students learn to love math. 
To Read Next:
Teaching Middle School
Sometimes, when I tell people that I love teaching middle school, they look at me like I’ve grown several new heads. They just can’t fathom what could be so great about it. I've taught middle school for 12 years, so I've had a bit of time to figure out what I like so much. It’s tough sometimes, but the challenge is part of what I love. Other teachers (middle school teachers?) agree: middle school is completely different from elementary and high school, but in a good way. If you don’t believe me, I’m not surprised. Read on to learn what I think are a few of the best things about teaching middle school. It’s Always Something New In The Young Adolescent Learner, Fran Slayers and Carol McKee, both former middle school teachers, talk about the middle school mindset. Those tween years are chaotic at best. Middle schoolers are going through so many changes in their lives, and that is reflected in their behavior in class. It’s a fun challenge to figure out how to keep their attention, appeal to their changing minds, and keep them engaged. Most middle school students like to play games and do activities that let them get up and move. They're independent and great thinkers and questioners; many of them feel free to make suggestions about how to change or improve an activity, which is wonderful, because I’m always looking for new teaching methods and activities. My students help me continue to become a better teacher. They’re Hilarious High schoolers can be just too cool to laugh at a corny joke and elementary schoolers are too young to get certain jokes. Middle schoolers are the perfect age for teachers to crack jokes. They have a great sense of humor and it makes it easier to joke around a little and play fun games as part of the teaching process. Many of them love to share their own funny stories and jokes; it's a great way to connect. I Help Shape the Future Yes, middle schoolers are going through plenty of changes with their minds and bodies, but middle school is the perfect time to help mold them for the future. Students in this age group still have the optimism of a child, but they are starting to think more like adults. They’re forming opinions of the world and thinking about their futures. I love being able to be a part of this process. For instance, if I can instill the importance of math in terms of their future career, they may learn to embrace math as part of achieving their goals. Of course, it’s always nice to hear from a student years later that something I said or did gave them the confidence to go for what they dreamed of. I Get to Teach Empathy No, empathy itself isn’t a class, though our school does have a program that gives us the opportunity to meet with students every week and discuss issues they may be having, especially as those issues relate to bullying. Middle school is the time that the bullies can really start making life hard for their fellow students. Our weekly meetings give students the chance to talk about these issues (and others). We have time to brainstorm ways to approach issues, talk about possible situations before they occur, and even role play how to deal with these problems. I think creating a culture of empathy in the classroom is vital to middle school development. It’s a chance to teach them to think about others and consider their actions. It also continues to help me be more empathetic. This is part of why I like to use games and puzzles in the classroom. It’s a chance for my students to work together and better understand each other. I’m A Role Model Middle school is an impressionable time. It’s also a time when students start to question authority. My students know that I’m firm, but fair. I'm empathetic, but I have high expectations and I make them clear. When they do something wrong, I call them out. Depending on the particular situation, I don’t simply tell them to stop; I explain why they need to stop. I tell them stories about myself and others. It makes me hold myself accountable, knowing that I’m a role model during a time when good adult role models aren’t always easy to find. Honestly, the best thing about teaching middle school is growing with the kids. They’ve helped me throughout the years to better understand myself and become a better teacher. For that, I’ll always be grateful. 
To Read Next:
Teaching Challenges
All teachers have to face a variety of challenges every day. But I’ve discovered that math teachers face a few unique issues. Despite how important math is, math teachers often face the attitude that math simply isn’t that vital to success, and it's okay to be "bad at math." Parents will come to conferences and willing admit they've always been bad at math. This problem is especially true as technology advances. Some of the biggest issues facing math teachers today are traditional reluctance and a society that lives on smartphones. Varying Levels of Prerequisite Knowledge Children learn in different ways, have different background based on both teachers and family, and have different experiences. This means I typically start the school year with a classroom full of students that do not share the same levels of prerequisite knowledge. In addition, students may have learned different approaches (or "short-cuts") to the same concept, like varying methods of adding fractions (the butterfly method - please don't teach it!). It’s important to complete some pretesting to assess what students know and learn about their methods for solving problems, in order to meet students' different needs. Connecting Math to the Real World I’m sure you’ve heard numerous students complain about how they don’t need to learn Algebra for the real world. I hear it quite often for all types of math skills. It’s one of the biggest issues facing math teachers. How do we connect math to a student’s life? It’s important to show students how math relates to their lives and the real world. For instance, talk about calculating a car’s gas mileage; creating a budget; leaving tips in restaurants and understanding how the tax is calculated; increasing or cutting back portions for a recipe; and analyzing how athletes train. Math is everywhere, but proving that is hard sometimes. Adding in fun puzzles and games that students could do as a hobby can help change the view of math as something that seems “too difficult” to something fun. Enforcing Learning Versus Computing A growing issue math teachers face is quickly advancing technology. When students have a math genius in their pockets (aka smartphone), why should they have to learn math? Why learn how to do a problem on paper when their calculators do it for them? While I know students would rather just let their phones do the work for them, I like to put them into scenarios that show them why it's important to understand how/why those answers are coming out of the calculating device. For example, when they start working at a job, how will they know if their paycheck is correct? Do they WANT to be sure they are getting paid what they should be? If they know how many hours they worked, and what their pay rate is, they should be able to figure out their pay. They should be able to calculate whether the amounts deducted from that check are correct. Mistakes do happen - they need to understand that and be able to verify the information they're given. In addition, they need to understand that the phone or calculator doesn't tell them WHAT numbers to enter to find a solution - they need to have the number sense and math logic to figure out what numbers they need to enter. Being a math teacher today isn’t always easy, and we need to work hard to overcome issues like these. 
To Read Next:
I taught elementary school for 12 years before moving to the middle school to teach 6th grade. While many 6th graders come to the middle school feeling nervous and unsure, most of them settle in fairly quickly and launch into that age of change that the tween/early teenage years bring. Middle school students are at an age where they want to explore everything, and for some, paying attention doesn’t come easily.
Keeping their interest and helping with the sometimes awkward transition between elementary school (where they were just kids) to high school (where the teens take over) isn’t always easy. I’ve found it takes a special kind of approach to keep middle schoolers engaged. Break Up The Monotony I know that school is partially about teaching students the value of routines. It keeps them on track and prepares them for being an adult one day. However, I fully believe that managing middle school effectively means breaking up those monotonous routines. For instance, in the middle of a lesson, I might randomly assign partners and have them do a quick pair/share or a brain teaser to cement that part of the lesson. I also stop for quick Q&A sessions. Many students won't raise their hand to ask a question during class, because they don't want to call attention to themselves or their need for clarification. But if I designate a few minutes as official QA time, they will. During these minutes, I allow them to ask me or ask a neighbor; sometimes asking a neighbor is more appealing because they don't have to ask in front of the whole class. If the neighbor also doesn't know an answer, then there's a "better" reason to speak up and ask me. As I circulate during "neighbor questioning," I can hear the types of questions they ask one another, which gives me an even better handle on their thinking. Take Downtime Breaks I’m not saying middle schoolers need nap time (though we probably all could use a nap break!) Downtime breaks are different. These involve giving the students a few minutes to simply process everything. Downtime also gives students time to shift their focus and reset. This is ideal when they’re frustrated over trying to learn something new. Instead of just pounding at a problem forever, a downtime break lets them step away and come back renewed. I’ve discovered it actually helps them learn more. Offer Engaging Activities Middle school minds work a bit differently than other ages. It’s considered a pruning time as the brain starts eliminating unused connections. This also explains why some middle schoolers seem so difficult to engage with. It’s not their fault that their minds are in a developmental period. My solution is to provide engaging activities. Since the average attention span at this age is 10-12 minutes, I make segmented lesson plans that fit in that time range. After each segment, I’ll get more interactive. I might play a game with them, do a quick group activity or challenge them with a puzzle. Middle school students tend to learn best with interactive methods, so this approach provides the best mix of traditional teaching and interactive teaching. Take A New Approach To Getting Their Attention I used to have difficulty at the beginning of the class period, getting students to settle and be ready to start math class (particularly because math isn't always a favorite subject - can you believe that?!) However, I now teach my students that as soon as they walk in the classroom, they work on their warm-up. Sometimes they actually do the warm-up at the beginning of class, but often the warm-up was homework, and their job is to go over the warm-up together and discuss any disagreements. This is about a 5-7 minute time period (depending on how on-time to class everyone is) that gets them focused immediately and gives me a chance to circulate and see who has questions. At other times, like during group-work, I use "Give me 5" to get their attention - I say, "Give me 5" and then count to five. When I get to 5, they are to be quiet and be giving me their attention. This technique is from the Harry Wong book, The First Days of School. I used this in elementary school, and when tried it out with 6th grade, it worked just as well! Every once in a while, students just get off-task. When this happens, I will sit down and just look at them (I refuse to raise my voice). It only takes a few seconds for a couple of students to notice my silence, and then they all become silent as well:-) Clearly Manage Progress Finally, I think it’s important for middle schoolers to always know where they stand in a class. I like to provide feedback to students to help them know how they’re progressing and show them which areas they may be struggling in. This gives them a chance to ask questions about trouble areas and talk to me about ways to improve their grades. For several years now, I have had students keep a tracking sheet in their binders. Every time they receive a grade, they record the points they earned and the points possible, and then convert that to a percent (this is great all-year practice for converting fractions to percents!). I teach them how to add ALL of the points (theirs and possible), to find their class grade at any given time. Grades are now available on the computer, but students often don't check that (their parents might), and some don't have computer access. Regardless of whether they check the computer system or not, I think it's important for them to know how to figure this out themselves, in order to understand exactly how the computer is calculating. Calculating for themselves can help them understand why the A they got on that 10-point quiz doesn't give them an A in the class if they already had a C on a 30-point assessment.....I might write more about this another time:-) One final piece of advice is to simply pay attention to your students. Managing middle school gets so much easier when you pay attention and interact with your students. They appreciate the extra effort and they’ll reward you by helping you understand them better. 
To Read Next:
|
AuthorHey there! I'm Ellie - here to share math fun, best practices, and engaging, challenging, easy-prep activities ideas! 
Select to receive 5 days of fraction resources!
Select to grab the free trivia cards:-)
Select to see on TPT
Select to see on TPT
Select to see on TPT
Archives
September 2021
|
