Each year, I tend to use early January as a time to reflect on where we’ve been and where we’re going in terms of the current school year. While we haven’t quite reached the middle of the school year, I consider this my “mid-year” reflection. I think about the mathematics content I have taught, the skills my students still need prior to the state-mandated tests and I consider my own personal teaching goals and how close I am to achieving them.
When reflecting on content, look at your district’s curriculum and determine how close you are to being right on track. If you’re like most teachers, you may have a bit of catching up to do. Don’t panic…remember, this is why it’s helpful to periodically evaluate where we are. Now, look at the lessons that still need to be covered and, if necessary, start prioritizing. Think about how you can integrate lessons and shorten lessons to cover content that is most critical for students.
It is likely that you are also thinking about the upcoming state tests. While content is critical for success on these tests, also consider other important test-taking skills that students need. In addition to learning the math skills, decide how you can help ease your students’ stress level. Begin infusing open-ending problem solving in to daily lessons. Provide tips for eliminating answers on multiple choice questions, and try to get students to feel confident and even excited about the test so that they don’t panic when the big day comes.
Finally, think about your own personal goals and how close you are to achieving these goals. Put together a rough calendar of how you might be able to reach your destination before the end of the school year. Use this time to gather your thoughts and develop a path for the remaining months of school. Don’t get overwhelmed by what you haven’t done. Instead, think about how far you have come and how good it feels to have a plan of action for the upcoming months.
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Like many of you, I am in the process of preparing next year’s budget and determining what materials will be needed to support student instruction. In addition to our typical order, we are thinking about investing in new elementary math textbooks. In NJ, the Common Core Standards were adopted and implementation of the new standards for Kindergarten through Grade 2 will begin in September. We feel it is appropriate to introduce a new textbook that will more closely align with the new expectations.
One of the challenges of textbook adoption is recognizing what comprises a quality textbook. Teachers tend to look for features with which they are most comfortable. These preferred features are likely part of their current textbook series, so teachers often select a textbook that is almost identical to the one they are currently using. In some cases, this is a completely acceptable outcome. However, we do want teachers to look for features that will be most beneficial for their students, not just those that keep them in their comfort zone.
To facilitate this process, I am going to use a textbook evaluation checklist with all of my teacher colleagues. This checklist provides un-biased suggestions of elements in the textbook that will be beneficial for all users. You may choose to use a checklist that you find online, or you may create a checklist that is specific to your district. Either way, it’s helpful to provide teachers with a guide that provides characteristics to look for in a new textbook and allows teachers to rate elements based on their importance. I found this checklist online, and I plan to use it as a template for creating a checklist that will meet our district’s needs. I think this tool is one that will increase teacher awareness as they look at textbooks, and I’m sure that teachers will emerge from the process confident that they selected a textbook that includes all the features that are necessary to increase student achievement.
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Teachers are always looking for ways to motivate students, especially at this time of year when it seems just a bit more challenging to crawl out of bed and head to school. So, it’s important to find ways to help students have fun in math class. Last year, I created “Mitten Math”, an activity that I used to help my 5th grade students practice long division. Now, if you’ve ever taught long division, you know that it’s not the most exciting topic to teach, and likewise, it’s not always fun for students to practice this skill.
In this activity, students practice four challenging long division problems in a unique way. Students receive the following materials: Mitten Math Recording Sheet, 8 Math Mittens (made from construction paper with holes punched in the “wrists”), and yarn. Four of the mittens have a division problem written on them; two of the mittens have a quotient written on them and two of the mittens are left blank. The students’ goal is to pair the problem mitten with its correct quotient mitten. Two of the quotients are provided to students, and two of the quotients must be filled after the problem is completed. All work is completed on the mitten math sheet, and once a pair is found, students use the yarn to tie the pair (problem and quotient) of mittens together.
A few things to think about...first, problems need to be selected so that students aren’t able to easily recognize the quotient by looking at the problem. This is part of the reason why I left two of the mittens blank. Students aren’t able to match all four pairs because they don’t know the value of the missing quotients. Second, this activity is great for differentiation. I created a different set of mittens for each of my students. You could do the same and base the problems on students’ ability levels. Or, you could make just a few sets of mittens based on different levels and group students accordingly.
The activity is relatively simple and the “fun” part doesn’t take up much class time, but it motivated students to work hard to solve challenging division problems and seemed more effective than giving them just another worksheet. Have fun!
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Here’s a little vignette from last spring. I was in a group of parents waiting to collect kids from a “new school” visit. The teacher was wrapping up the day with an outdoor game where kids left and rejoined a circle based on some algorithm. Physical math in the sunshine, with lots of happy noise and an improbable amount of focus.
I exchanged who’s, where’s and how old’s with the parent next to me and we talked briefly about work. She then said, “You know, I think I’ve done it all wrong. I have an MBA in marketing, I worked for a major hospital group, and I had my own company for a while. But I really wish I had been a teacher.”
Now those of you in the trenches may say that was the spring weather talking. Who wouldn’t feel that teaching was blessed work, when the task was an outdoor number game on a gorgeous day?
But teachers: know that the meaning underlying your work is envied by many, MANY ordinary civilians. Your most mundane everyday activities have the potential for purpose that few jobs can offer.
We are in awe of you – your endurance, your attention to the details that matter, your endless patience when asked to handle the same problem over and over and over again. All in the same day.
But in that same day, something or several somethings may have happened that have lasting significance. And that is what we find most awe-inspiring of all.
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Recently, I’ve been asked to work with a few 5th grade students on place value and rounding. I can’t help but recognize the significance of the fact that they are almost half-way through their 5th-grade year and still struggling with place value. It made me start thinking about why students struggle with this concept and how important it is that they receive a strong foundation in place value in the elementary grades.
We all recognize the need for students to develop number sense – the ability to recognize how patterns and relationships exist between numbers. A major part of this, though, is a student's understanding of the value of digits relative to their place in a number. For example, many students don’t see the number 24 as being 2 tens and 4 ones. They see the number as a 2 and a 4 together. They recognize that 24 is greater than 15 because the 2 (in the 24) is greater than the 1 (in the 15), but they can’t explain why. When students start regrouping in subtraction, many are taught to follow a process: cross out the number in the tens column, make it one less and put a 1 in front of the number in the ones column. What many students fail to see, however, is that they are regrouping 1 ten for 10 ones. Some of this can be helped by using appropriate math vocabulary and actually saying, “We are going to regroup 1 ten for 10 ones…” and so on. Using visual models also helps students see what is happening with the math. The ideas get even more complex when we start considering decimal place value. Students who do not have a firm grasp on whole-number place value are going to really struggle with parts of a whole.
Fractions, decimals, multiplication, division…the list of skills that require a strong foundation in place value goes on and on. We need to be sure students understand the why behind their work, rather than relying on tricks to help them complete the process. Think about this as you work with your students. Start to identify some misconceptions that your students are having and search for ways to help alleviate these problems. You’ll be surprised how far it will take them in the long run.
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Students from Shanghai,China posted the top scores in math according to test results released last week by the Program for International Student Assessment (PISA), which compares the performance of 15-year-olds from 60 nations and 5 regional areas. Singapore and Hong Kong, China ranked second and third, respectively. The United States tied for 31st.
News headlines announced that Shanghai "stuns experts" and "owns the PISA," but it's actually not so clear cut. First, how is it fair to compare the United States--as a country--with selected regions in China? Secondly, do students of all levels in other countries test on the PISA (as is done in the U.S.) or are only the high achievers taking the test?
The New York Times, for instance, reported:
"For one thing, Shanghai is a huge migration hub within China. Students are supposed to return to their home provinces to attend high school, but the Shanghai authorities could increase scores by allowing stellar students to stay in the city, he said. And Shanghai students apparently were told the test was important for China’s image and thus were more motivated to do well, he said."
Despite the questionable ranking system, some interesting trends emerged from the report:
- Regardless of their own socioeconomic background, students attending schools with a socioeconomically advantaged intake tend to perform better than those attending schools with more disadvantaged peers.
- GDP per capita did not appear to matter much: Korea, which is the best-performing Organization for Economic Cooperation and Development (OECD) country, also has a GDP per capita below the OECD average. While there is a correlation between GDP per capita and educational performance, this predicts only 6% of the differences in average student performance across countries. The other 94% of differences reflect the fact that two countries of similar prosperity can produce very different educational results.
- The most successful school systems grant greater autonomy to individual schools to design curricula and establish assessment policies, but these school systems do not necessarily allow schools to compete for enrollment.
Though the focus is often on numbers and rankings, maybe it is these buried lessons of the trends (as expressed by former Vermont superintendent, William J. Mathis) that are most valuable.
Image Credit: OECD Website
Each year around this time, I wait for PNC to release its annual Christmas Price Index. This isn’t just a standard listing of price increases or decreases; it focuses on the current prices of the items listed in the 12 Days of Christmas song. Why do I wait so patiently for the release of this information? Because I think it’s so interesting to integrate math into this whimsical song that we all know so well. It’s fascinating to think that there actually can be a price attached to each of the seemingly silly items mentioned in the song.
Depending on the level of your students, you can create some fun activities dealing with percent increase or decrease and even trends in the economy. On the website, there is an educator link that will give you some ideas. Activities include games that students can play online. One game has students matching a price with an item. It’s great to see how students use logical reasoning and estimating skills to complete this task. If none of the activities presented online suit you, have fun creating your own activities. In the past, I’ve had students find the percent increase or decrease of each item over two consecutive years (this requires you to provide this year's and last year’s prices without the percent increase/decrease provided on the site). I’ve also had students estimate the total cost of all of the items and then compare it to the actual total cost. Usually, they are quite surprised about how generous the gift-giver is to his true love!
It seems that the last few days before winter break present a challenge to both teachers and students. We’re all ready for a break, and it’s tough for everyone to focus on teaching and learning. However, integrating activities using a tool such as the PNC Christmas Price Index can keep the learning alive and motivate your students to do lots of math. Sounds like a nice little holiday treat for all educators!
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I recently wrote about strategies that can be used to assist non-English speaking students in the mathematics classroom. While attempting to keep these students on par with the rest of the class is important, it’s also critical for these students to be experiencing a positive educational experience. Unfortunately, it’s often too difficult for these students to keep up with the rest of the class, so in order for them to be successful, their work must be differentiated.
As with any student, it is important that English-language learners are given work on their level so that they may move forward along their individualized educational path. Therefore, if a 6th grade student is working at a 2nd grade level, he or she must be given work on that level. Teachers must also be sensitive to students’ specific language struggles in mathematics. Many people think that math is just numbers, but there is a tremendous emphasis on problem solving. Word problems present an additional challenge for students who haven’t mastered the language. Teachers need to be aware of these struggles and ensure students have mastered both the mathematical content and language before integrating the two.
Beyond individualizing content, teachers must think about the best way to grade these students. Clearly, many would fail if simply graded on grade-level content. Ideally, students will succeed with content at their level. However, if assessments must be given on grade-level, a fair grading policy must be instilled. In my district, teachers are encouraged to provide a narrative, rather than a letter or number grade. By doing this, progress can be noted without unfairly judging students on content they may not comprehend. Providing positive feedback rather than a failing grade is more likely to motivate students. Helping students maintain a positive disposition so that they may stay motivated is so important at this point.
Each district must work collaboratively to develop a plan that is most appropriate for their situation. The key point is that a plan is indeed necessary. Don’t let these students slip through the cracks!
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I am the coordinator of my school’s I&RS Committee (Intervention & Referral Service), a state-mandated team that provides teachers with strategies to help students who are struggling academically or socially. Recently, many teachers’ requests have been for strategies to help English Language Learners in the classroom. Because my focus is on math instruction, I tend to offer the most support in that area. Here I’ll offer some suggestions about how you can improve math instruction for those students who speak English as a second language.
- Develop Vocabulary – This includes both general academic vocabulary and math vocabulary. Many times, words that we assume are simple mathematical terms can be confusing for students developing the language.
- Use Concrete Objects and Pictures – We've learned that moving from the concrete to the pictorial to the abstract is a successful strategy for any learner, but it is especially critical for those who have not yet mastered the language. These students need to see the math before they can understand the terms and symbols used to represent the math.
- Encourage Collaboration – Often, students who are just learning the language are timid about participating and communicating with others in the math class. Provide non-threatening opportunities for these students to work with others who are at their level so they can practice speaking about and listening to mathematical ideas.
- Keep Problem-Solving Simple – Think about how much average students struggle with problem-solving in math. Now, layer on top of that the challenges of a student who has not yet mastered the language. While it is important to give all students opportunities to apply the skills they have learned, ESL students must have a good grasp on the computational aspects of a problem, as well as the vocabulary in the problem before these two aspects can be successfully integrated.
I am by no means an expert in ESL instruction. However, I have learned that simple tweaks can really improve the success rates of these students in the classroom. Please feel free to share your ideas and the strategies that you have used to help language learners progress in your class.
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My husband discovered today that it’s no fun going holiday shopping with a math teacher. While working my way through the hustle and bustle, I made two discoveries that reminded me how many adults don’t feel comfortable with routine math. First, I noticed that almost every store that I enter these days includes discount price lists for all of their sale items. So if a rack is marked 25% off, next to that sign is another listing the sale price depending on the original price of the item. I admit I have used these guides from time-to-time, but this hasn’t alleviated my frustration about the fact that they are available. Like the convenience of calculators on cell phones, these signs have made it so that customers really don’t need to know math to budget while shopping. It used to be that this scenario is one that would motivate students to learn basic percentage operations. Now, even that simple task can be completed without much thought. Again, it’s not that I don’t appreciate factors of convenience; I just wish our society would continue to promote the need for mathematical competence.
Second, I overheard a conversation that I’ve heard between a customer and a salesperson several times before: “But the item is 50% off and I have a 25% coupon, so that means that it’s 75% off!” Many people understand that in this scenario, the item is 50% off and then 25% off that price – not 75% off the original price. However, some who are less skilled in working with percentages fail to see the difference between the two scenarios. Students need opportunities to investigate similar situations so that they fully understand the financial implications of an incorrect calculation.
I know that the frustration that I felt today is not isolated to this time of year, but there’s something about the stress and crowds during December that heighten my awareness of the need for people to be more mathematically literate. So I’m asking you, my fellow educators, to help our students understand how computational fluency and strong mental math skills can make every aspect of our lives – even holiday shopping – more pleasant.
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