Trapezium Blog

What elementary instruction misses about fractions

amciver@trapeziummath.com (Angela McIver) — Wed, 04 Oct 2023 15:43:04 GMT

As I was meeting with my team this morning to refine our unit on fractions, we discussed how even the brightest students become confused about fractions over time.

Studies have shown that students make little progress in their understanding of fractions between 4th and 6th grade (when fractions are first introduced and then expected to be mastered). This may be the result of the unintended consequences of well-meaning instruction.

Below are 3 very common ways students develop misunderstanding of fractions because of the way fractions are taught in elementary schools.

Misconception #1

The larger the denominator, the smaller the fraction

This is probably the most common misconception students develop when it comes to fractions. Although the statement is partially true, it only relates to unit fractions (fractions where all the numerators are 1). We call this pizza/pie thinking because teachers often resort to a pizza or a pie to explain this concept, usually with accompanying drawings. I often hear teachers say “Think of a pizza. Would you rather have a piece of a pizza cut into four slices (¼ of a pizza) or 8 slices (⅛ of a pizza)?” Once students latch on to this way of thinking, they apply it to every type of fraction regardless of the numerator. This thinking can be demonstrated in this video of a high school student when asked to order four fractions based on their relative size. To counter this type of thinking, it is important for teachers to make explicit connections between comparing unit fractions with all other fractions.

Misconception #2

Fractions exist on the workbook page (but not in real life)

A fraction is a tool used to describe problems, situations and phenomena that exist in real life. But most students leave elementary school with a belief that a fraction is a problem that exists on the page of a workbook or computer screen. And, our inability to connect the learning of fractions to real world scenarios is hampering student understanding. I believe this is directly tied to many elementary teachers’ fear of math when veering too far off the page (or computer screen) can expose their own fragile understanding. In this article about student math understanding after the pandemic, a group of teachers learn of how one teacher with math anxiety often skips math concepts to leave for her students’ teachers the following year and others agree. If this happens two or three times in a student’s time in elementary school, it can have an enormous impact on their ability to transfer understanding from the page to “real life.” As math concepts become more complex in the upper elementary grades, teachers tend to stay close to the textbook, unintentionally denying students the opportunity to develop a deep and flexible understanding of fractions.

Misconception #3

A Fraction is a fraction, a decimal is a decimal and a whole number is a whole number

Because whole numbers, fractions and decimals (as well as percents) are often taught in separate units with separate practice problems, students can leave elementary school believing that these are completely separate concepts. Instead, students should build on the understanding that all whole numbers can be written as fractions or decimals (although not all decimals can be represented as fractions - these are irrational numbers). Care should be taken to make sure students develop the fluency to move between these different representations.

Understanding the ways that misunderstanding can develop in students’ thinking can help teachers become more confident and competent teachers in their classrooms. Supporting the deepening understanding of fractions among teachers may help address these gaps.

Mathnasium vs Kumon vs Trapezium Math: Which Program is Better?

Thu, 23 Mar 2023 07:22:40 GMT

My career has been motivated by curiosity about how children learn math. I have interviewed hundreds of students across the country from kindergarten to college about their experiences learning math. Through my research I found that few students are provided the rigor and repetition necessary to develop strong math foundations. I also found that when rigor is provided, it is neither engaging nor confidence-building for students.

As a result, many parents look for alternative and supplementary math programming. When surveying the options for supporting young math learners outside of school, many parents and families come across well known and established math tutoring companies; Mathnasium and Kumon. While these programs have credibility and work for some students, their approach replicates the teaching style used by most schools, using worksheets and workbooks. As a parent who has signed my children up for both of the programs, I have found that neither of these alternatives addressed the root causes of their challenges, nor did they provide excitement or engagement around math.

I started Trapezium Math Club out of my home in 2009 because my children’s needs were not being met by their elementary school math curriculum, or support from other math enrichment programs like Kumon and Mathnasium. I noticed the way that math caused my children stress and confusion, and I knew they were not alone. When we founded Trapezium Math Club in 2009 our goal was to provide programming to students that was highly engaging, confidence building and prepared students for middle school math and beyond. Our curriculum, like Kumon and Mathnasium, aligns with common core standards, so that students see a direct correlation between what they are learning with Trapezium and what they are learning in school. Unlike Kumon and Mathnasium we take worksheets out of the equation and engage students in developmentally appropriate ways: through games, movement and hands-on activities. We believe in cultivating an entirely new approach to working with young students in math that engages them creatively, socially, physically and intellectually.

Our highly qualified Math Club Leaders are trained to facilitate curriculum that has been developed, and kid tested, over the last 15 years. The curriculum is designed to establish strong math foundations through scaffolding and repetition. Club Leaders are also trained to work with students on social, emotional learning and building positive and trusting relationships with their students. Math Club is an hour long, virtual, weekly meet up with groups of up to 4 students and 1 Club Leader. Students are grouped based on proficiency. Accompanying the club is a Math Club Kit, which has manipulatives that are used throughout the club.

Our approach at Trapezium radically transforms the way that young math learners engage with math, fostering a positive association with math, cultivating confidence and building durable relationships.

Why We Skip Count: And Why We Time It!

amciver@trapeziummath.com (Angela McIver) — Fri, 22 Apr 2022 14:05:09 GMT

As a former middle school math teacher, one of my biggest challenges was teaching pre-algebra to students who had not developed automatic recall of basic facts. The students who struggled most in my classes were those who could not quickly do math in their heads. Most elementary schools do a poor job of developing this skill.

When a student must stop to figure out a basic math fact before completing the rest of a problem, it has a compounding effect and acts as a stumbling block to learning pre-algebra and algebra. Often, they must be able to recall multiple math facts within a single problem. For example, if a child has to stop to count, or make groups to figure out what 8 x 6 is, that child is going to become frustrated and quickly fall behind. This is comparable to a child who must stop to sound out words they should know by sight when reading.

Years ago, my team and I sat down to figure out how to teach young children multiplication facts so that they learned them quickly and understood them thoroughly. We discovered that the standard “Minute Math” worksheets ubiquitous in classrooms all over the country, did not help improve basic fact recall for those students who were stuck in the first place. In other words, more “drill and kill” did not improve their mastery. We went back to the drawing board and realized that the foundation for learning multiplication was skip counting. We understood that if we could help our students become fluent in skip counting all of their multiples, they would quickly master their multiplication facts.

We tested how much and how fast our students could count. We wanted to build fluency by finding an ambitious yet attainable time to complete a series of “skips.” We decided that for our multiples, students must do 15 skips up and back. Then we began testing the time it should take a student who is considered fluent to complete these tasks. We found that on average, students can complete an entire series (up and back) in 15 seconds or less with practice. However, we set our minimum goal for fluency at 30 seconds to accommodate outliers who may have learning challenges.

One way to build your child’s fluency and confidence is to practice skip counting at home with them. This simple activity can be done anywhere and takes only 30 seconds. For many children, this will be the first time that they have to demonstrate fluency in a math skill. Be patient, it will take many, many weeks of practice for your child to become fluent. This is a confidence-building activity that reinforces the concept that we are not born “math people” but become proficient by regular practice with suitably challenging activities.

We believe in setting a high bar and helping children get over it.

The Do’s and Don’ts of Parent Teacher Conferences Make this Year Great for your Child and Their Teacher

amciver@trapeziummath.com (Angela McIver) — Fri, 19 Nov 2021 18:24:57 GMT

For many teachers, the upcoming parent teacher conferences will be the first face-to-face meetings with parents in almost two years. Here are some Do’s and Don’ts as you prepare for your parent teacher conference.

Questions to Ask During the Parent Teacher Conference

Parents can be fraught with anxiety when it’s time to discuss their child’s performance with their child’s teacher. Much of this anxiety can be alleviated if the parent goes in prepared with questions to ask during the parent teacher teacher conference. Asking questions is the best way to shape the conversation and ensure you address all of your concerns with your child’s teacher.

You can gain insight into your child’s class by asking the teacher questions about the classroom dynamic. Simple questions like, “What is the most challenging part of your day?” Can lead to valuable opportunities for parents to help the teacher create a positive learning environment. For instance, your child’s teacher may say “I teach math after lunch. It’s difficult because students are far less attentive at that time. I lose 15 minutes of instruction time each day trying to get everyone settled down for math.” This information lends itself to a useful conversation with your child. You might say, “I understand that it’s hard for your class to focus after lunch when you do math, why do you think that is? What do you think you and your classmates can do to address this?” I guarantee, if every parent in your child’s class had that conversation, math after lunch wouldn’t be so difficult to teach and a lot more learning would happen.

Another question you might ask the teacher is how you as a parent can best support them. Their answers may surprise you. They’ll undoubtedly be happy to know that you believe supporting the teacher is important but most of all they will feel heard.

What Not to Do During the Parent Teacher Conference

Don’t be a Demanding and/or Unreasonable Parent

Please understand that most teachers care alot about your child's progress. Still, some parents can be demanding and unreasonable. So, I’m imploring you - don’t be that parent! Teachers have a set of expectations. Do you know what is expected of your child? Is your child's behavior in line with those expectations? When I was a teacher, I remember a parent telling me that she was going to schedule a meeting with her lawyer, one of the School Board members, the superintendent and me because I wasn’t willing to change her child’s grade from a C to something higher (her child didn’t turn in a single piece of homework the entire term and I thought giving him a C was generous). While this is an extreme example of the demanding and unreasonable parent, every teacher I know can share stories of parents from hell during this time of year. Don’t be THAT parent!

Don’t blame the teacher for the curriculum!

I say this - especially when it comes to elementary math. Your child’s teacher is required to teach the mandated curriculum whether they agree with it or not. Many of the lessons that we see in elementary math curriculum are confusing. They are often developmentally inappropriate and move far too quickly for any real mastery to happen. Your teacher knows this and is equally frustrated.

Instead, you might ask the teacher “What is something in the curriculum that you wish you had more time to work on with students?” This will open up conversations about what you may be able to do at home to support the challenges our teachers are facing. While teachers are required to teach the mandated curriculum, they have a treasure trove of activities that they’ve collected over the years and are happy to share.

Don’t ask for special treatment for your child! This is a big one. Please don't ask your child’s teacher to create different lessons or activities because you believe they are gifted, not being challenged and need more . I am the first one to agree that children should be provided with opportunities to be challenged at their level, but this is an issue for the school (or the district for that matter). Teachers have so much on their plates just planning lessons for an entire group. They work evenings and weekends making engaging activities and lessons for their students; they spend money out of their pockets to ensure that their students have what they need. The last thing they need is a parent asking for special work for their child. DON’T BE THAT PARENT!!

Finally, I encourage you to remember that every teacher has been under an extraordinary amount of pressure after a year of remote learning. When teachers entered their classrooms this fall, they welcomed children who - for many reasons - have also been traumatized. Whether from a decline in mental health due to a year of being away from school and regular routines, or from the traumatic loss of a loved one to COVID-19. Our teachers welcomed a class of students that looked remarkably different from those in their classrooms in March, 2020. Many of our teachers have had to deal with their own trauma that COVID-19 has wrought. Additionally, schools and districts are facing an unprecedented level of teacher burnout and are working with challenging staffing shortages. This means that your child’s teacher may have a larger class than normal or is required to cover classes that don’t even have teachers. And many teachers have lost valuable prep time.

Given that context, let’s all agree to enter these parent teachers conferences with a mindset of love, patience and grace for our teachers. Be THAT parent!

Angela is a former middle school math teacher and founder of Trapezium Math - a company dedicated to creating joyful, confidence-building math experiences for children, teachers and parents. From 2018 to summer 2021 she was a member of the School Board for the School District of Philadelphia .

Reimagining Schooling in a Post-Pandemic World

amciver@trapeziummath.com (Angela McIver) — Wed, 07 Apr 2021 14:21:07 GMT

It’s been more than a year since U.S. schools closed and children were relegated to remote learning from their bedrooms and kitchen tables. And, while much attention has been given to what students have lost, little attention is given to what has been gained. If there is one thing the pandemic has taught us, it’s that education models can no longer be based on a one-size-fits all approach. As educators move to re-open schools, School Boards across the country must use what they’ve learned to encourage Districts to reimagine schooling for every student.

What We’ve Learned

We’ve learned that an 8-hour school day–or even a requirement that students attend school in person every day–is no longer the only learning model for success. A well-thought asynchronous learning program provides opportunities for schools to reduce class size and provide more focused instruction for all students. This is not the hybrid model of the pandemic–where some students viewed their teacher on their computers from home while others were attending face-to-face learning. This would be a new and improved hybrid model where students are divided into cohorts with some students working independently from home while their counterparts receive intensive small-group instruction at school. This reimagined “flipped classroom” can be most impactful for high schools in large urban school districts where class size is untenable and student need is high.

We’ve learned that technology can provide access to rigorous coursework like Advanced Placement and International Baccalaureate courses to students whose home schools do not provide these opportunities. Creating highly engaging remote classrooms can bring these classes to any student who wants them. In large urban school districts, re-imagining school can mean creating learning hubs that serve many schools. State-of-the-art science and computer labs with classrooms can be housed in regionally designed learning centers with students logging in remotely for lectures, and venturing to their regional learning center for labs. No longer do students (or teachers for that matter) need to be tied to a particular school.

We’ve learned that distance education has given children with learning difficulties opportunities to learn without classroom interactions that can be extremely stressful. Parents of students with anxiety disorders and attention deficit/hyperactivity disorder have reported that their children have thrived and gained confidence during virtual learning. Anecdotal data also suggests that many of these students would benefit from some form of distance learning when schools reopen. Examining these models and how they have been successful in accommodating students with different learning needs should be a major factor in driving decisions in the upcoming school year.

We’ve learned that there are large disparities in resources and opportunity for well-resourced school districts and their less-resourced counterparts. While much of this inequity is structural and requires an overhaul in how schools are funded, there are ways that large urban districts can use lessons from the pandemic to get closer to parity.

There is an emphasis on getting back to the way we were, but I argue that we should be moving toward something better. Doing so will mean considering what students and teachers have gained during the past year and imagining something bold. Students from districts that are willing to think creatively and commit to being transformative will benefit most from a post-pandemic school environment. The most successful districts will be bold and fearless in creating better schools for all.

How the Pandemic Saved Trapezium Math Club

amciver@trapeziummath.com (Angela McIver) — Mon, 20 Jul 2020 17:47:00 GMT

The new year started off with such optimism. . . At math club we had commissioned a new Mathemagic play to be debuted in March. We were excited about the Spring Monstermathathon and had solidified our plans for summer camp. But, two seismic events turned everything upside down and forced us to change direction, resulting in the decision to close Trapezium Math Club ... and then to re-open it!

The first blow happened in February when we were notified by our landlord that our lease would not be renewed for September. Our space - home of Trapezium Math Club for 6 years - was being turned into a gym for the residents in the building, a casualty of gentrification. When considering my options, the numbers just didn't work out. Finding a space with reasonable rent in our neighborhood was not feasible. I decided to close Math Club and focus on other parts of our business ( Dinner Table Math and Trapezium Math for Schools) .

And then, the second blow. On March 13th the School District of Philadelphia closed all schools as the state issued a stay-at-home order. In an instant, our revenue from Math Club and Trapezium Math for Schools came to a grinding halt. With no revenue coming in and no promise of reopening, I had to lay off my staff.

But clouds have silver linings. The first came in the form of a PPP loan that allowed me to bring my staff back to work for 8 weeks. The second came with my appearance on Good Morning America . The exposure (and gift from Sofi) gave me enough money to make payroll for another 6 weeks.

With everything about our business model thrown out (no Trapezium for Schools if schools were closed and no math club with no space), we had to come up with a new plan. We decided that the best path forward was to focus on Dinner Table Math and to bring Trapezium Math Club back. But this time, Trapezium Math Club had to be online.

Since the beginning, our philosophy has been to provide technology-free experiences that build confident, fearless math learners in fun and engaging ways. But since we were in the middle of a pandemic, we had to embrace technology in order stay alive. The challenge has been daunting. We've gone back to the drawing board many times after focus groups with math club students yielded amazing insights about online learning. For instance, we've learned that children need something tactile to accompany online learning - a box of materials that is used as part of instruction. We've also learned that younger children need as little technology as possible with short, highly engaging sessions that only involve a camera.

In many ways, it feels like we are a start-up with opportunities to create a scalable business that focuses on our core priniciples - providing rigorous math to young learners in fun, highly engaging ways.

So that's how the pandemic saved Trapezium Math Club. Stay tuned for Math Club 2.0 launching in September.

#onlinemat h #elementarymat h #homeschoolingmat h #homeschoolmat h #funmath

What Math Instruction Can Gain From Reading Research

amciver@trapeziummath.com (Angela McIver) — Sun, 17 Feb 2019 18:44:59 GMT

I often ask these students to describe what’s going on in their head when they are struggling with a math problem. I interview students who struggle in math. The students I interview range in age from elementary and middle school to adult learners in job training programs. I give students simple elementary math problems and ask them to explain how they would solve them. While these interviews have fundamentally changed the way I think about how we should teach math to struggling students, my biggest “aha” moment didn’t come from the interviews, but from a day of volunteering in my youngest daughter’s kindergarten class many years ago.

My daughter’s kindergarten teacher, Ms. Silver, was a tiny woman with an enormous enthusiasm for her craft. One day, during a volunteer shift in her class, I had an opportunity to sit in the back of the room and listen to her teach a class of captivated children. She was engaging these students in a conversation about schema. After reading the students a story, she asked them to think about their own schema and then share with the class. A lively conversation ensued and I was left with the question “What is schema”?

Back home, a quick Google search revealed that schema is a theory of reading comprehension suggesting that in order for children to be successful readers, they must bring some prior knowledge to the experience. This prior knowledge helps a student better understand what they are reading. According to schema theory, the more prior knowledge a student has, the better their reading comprehension. It was in that moment I realized that what my struggling math students needed was a schema.

For several years, I’ve been trying to articulate something that I believe is missing from the students whose thinking I’m trying to understand. The best way I can describe it is an inability to imagine… an inability to connect with something “in their head”. I often ask these students to describe what’s going on in their head when they are struggling with a math problem. And, most often, these students are unable to draw upon any images to help them make sense of the math. I now believe it is because they are not being given opportunities to develop a schema. Often schools cut enrichment classes, athletics and field trips to focus on more math instruction. But, I believe the elimination of these activities is contributing to their math illiteracy.

Once, when I was interviewing a middle school student about his math understanding, it became very clear that he understood deeply, the concepts of area and perimeter. I asked him to describe what images he was using to help him solve the problems I posed, and he spoke about helping his father in his native Guyana, make bricks out of mud to build houses.

Once, while conducting a professional development with a group of teachers who were complaining about their students’ lack of number sense, one teacher spoke up and said, “I have two girls in my class who run track and they are the only students who have very good number sense.” This teacher went on to explain how these girls used their race times (measured to the hundredth of a second) to make sense of a lesson on comparing and ordering decimals. Now those girls have a schema!

The use of a schema needs to be taught in elementary math classes as explicitly as it was taught to my daughter and her classmates in reading. But more importantly, struggling students (especially students from low-resource schools with whom I am most familiar) need opportunities to develop their schema through enrichment activities that are a given for children from more privileged backgrounds. I am not arguing that if students take art or music or play on a sports team their test scores will improve. I am arguing that if students have opportunities to develop their musical, artistic, or athletic side they are also creating prior knowledge that teachers can draw upon to help them become fearless, confident math learners.

#mathlearning #elementarymath #dinnertablemath #urbanschools #lowincomestudents

Mulan and the problem with elementary math

amciver@trapeziummath.com (Angela McIver) — Mon, 04 Feb 2019 18:41:54 GMT

When I run professional development sessions for teachers, I often ask them “What do you own?” What I really want to know is, “What skill or math content do you own as a teacher and can say - with confidence - that your children will have mastered by the time they leave your class?”

The most important thing I’ve learned as an elementary math teacher is that children need to be exposed to a concept over and over and over again before it is mastered. I often tell teachers “Decide how much time you think you will need to teach a concept and multiple that by 10. That’s how much time you actually need”. And, this is the main reason why most elementary math curricula don’t work!

When my eldest daughter was about 18 months old, she saw a video of the Disney animated film Mulan and was mesmerized. From that point on, it was the only video she wanted to watch and she saw it every Saturday until she was about 3 years old.

Mulan is based on the Chinese legend of a young woman who posed as a man in order to join the Chinese Army and fight the Huns. Disney turned this legend into an animated film for children in 1998. At the beginning of the movie, Mulan is a young girl who does not seem to fit into the traditional gender roles associated with ancient Chinese culture. When the Huns attack and the emperor drafts all men to report for military duty, Mulan runs away and secretly joins the army disguised as a man. This all happens in the first half hour of the film and the remainder of the film chronicles her adventures as a young woman attempting to keep her secret from the men with whom she is drafted.

The last time our daughter watched Mulan was a Saturday morning in the spring after her third birthday. By this point, I would say that she had seen the full length film at least fifty times (I’m being quite conservative here). As usual, she was mesmerized. But, this time, while the closing credits were rolling, I stood in the doorway and observed her. She was staring into space with her hand on her chin. She was clearly in deep thought. After a few moments of contemplation she said out loud (to no one in particular) “Mulan is a girl!” After that day, my daughter was finished with Mulan. She finally understood it and was ready for her next movie.

I call moments like the one described above “Mulan moments” and I’ve observed many of them while teaching young children elementary math. It drives home the point that children need a lot of exposure with something before it “sticks”. The most important thing I’ve learned as an elementary math teacher is that children need to be exposed to a concept over and over and over again before it is mastered. I often tell teachers “Decide how much time you think you will need to teach a concept and multiple that by 10. That’s how much time you actually need”. And, this is the main reason why most elementary math curricula don’t work!

I’ve interviewed countless children who have entered middle school with very fragile understandings of concepts that should have been mastered in elementary school. I believe this is because the most popular elementary math curricula cover too much content for students to ever master a single thing. These programs do far too much, far too quickly and do not give enough time for young children to learn content deeply. Many of these curricula are based on the belief that “spiraling” (a theory in which students are introduced to a concept that returns again and again throughout the curriculum) is an effective mechanism for building mastery. But spending one or two days on a concept before moving to another simply causes confusion. When that concept appears again in the curriculum, it is as if they had never learned it the first time.

When I run professional development sessions for teachers, I often ask them “What do you own?” What I really want to know is, “What skill or math content do you own as a teacher and can say - with confidence - that your children will have mastered by the time they leave your class?” What is surprising is that most elementary teachers cannot answer this question with a large degree of confidence. It's because math programs do not spend enough time on any concept to develop full mastery.

But, math mastery is happening in spite of elementary math programs. Through my research, I have found that students who leave elementary school with strong math foundations, do so because their parents have invested extra time and/or money to help build the foundation at home. These children succeed in spite of the elementary math curricula.

This point is driven home by a story I'd like to share of a good friend who sends his child to private school. One day he asked me what he could do for his fourth grader who was struggling with math. I suggested he send him to one of the math tutoring centers in his town. When I followed up to see how his son was doing, he told me that when he asked his son how it went, his son said “Great! All of my friends [from his elite private school] are there.” Even parents who are willing to shell out a lot of money to send their children to private school recognize that math programs in elementary school are not sufficient to build strong math students.

My daughter had another “Mulan moment” about a year after starting piano lessons when she realized that the notes on the page correlated with the keys on the piano. Up until that point things didn’t quite make sense to her, but she found a way to fake it until they did. I believe that this is happening to children all over the country when they engage with elementary math programs that don’t give enough time for things to “stick”. Make no mistake, there are no “Mulan moments" in elementary math!

#elementarymath #theproblemwithelementarymath #mathcurriculum #learningmat h #dinnertablemat h #everydaymath #envisionsmath #mathinfocus

The Top 3 Math Skills Students Should Master (But Don't) in Elementary School

amciver@trapeziummath.com (Angela McIver) — Fri, 07 Dec 2018 18:38:13 GMT

I used to believe that older children who struggle in math do so because they did not master what was taught in elementary school.

I have interviewed hundreds of students all over the county about their understanding of basic math concepts. What I’ve learned in these interviews has fundamentally changed the way I think about teaching and learning math. I’ve learned that students are failing to find success in algebra and beyond, not because of the math they fail to learn in high school but because of the math they fail to learn in elementary school.

In my years since completing graduate school, I have worked with hundreds of middle and high school math teachers to share what I have learned about the ways students misunderstand basic math. As part of my work with these teachers, I always ask what elementary math skills they value most. I often phrase my question this way "If there were only 3 math skills that children could master by the end of elementary school, what would you want those math skills to be?" Through these conversations, I have discovered a pattern that has been reproduced consistently in workshops I have conducted across the country.

At the outset of my workshops, I ask participants to provide an elementary math skill they believe students should master by the time they leave 5th grade. I record the skill on chart paper and then ask the next teacher to offer another skill. Each teacher must provide a new skill to add to the list. At the end of the exercise, we often have 20 or more discrete math skills listed (such as, telling time on an analog clock; converting units of measure, algorithms etc).

At this point, I tell the participants that they must now take this list and come up with the top 3 elementary math skills as a group. In the more than 10 years that I have been conducting these sessions, the answer NEVER changes. The Top 3 elementary math skills (as determined by middle and high school math teachers) are ALWAYS:

Basic Fact Automaticity- Students should “see it/know it” for all basic addition subtraction, multiplication and division facts. (This is the equivalent of sight word recognition in reading.)
A deep and flexible understanding of fractions and operations with fractions (addition, subtraction, multiplication and division)
Strong reasoning skills (as in “does this answer make sense to me”?).

Unfortunately, this list has NEVER been reproduced when I conduct the exact same exercise with elementary school teachers. In fact, the “Top 3” list as determined by elementary school teachers is different in every workshop that I conduct. So, not only are elementary school math programs failing to align with middle and high school math teacher expectations, they also fail to align with each other. As a result, students are experiencing very different math programs (even when they are using the same curriculum) simply because what is valued is highly specific to the school or teacher.

I used to believe that older children who struggle in math do so because they did not master what was taught in elementary school. I now believe that these students struggle in math because what is taught in elementary school is often arbitrary and not at all aligned with middle and high school math teacher expectations.

A note about me: I completed my PhD at the University of Pennsylvania’s Graduate School of Education. My dissertation Understanding the Numerical Reasoning of Middle School Students focused on understanding why so many students struggle with math after leaving elementary school. I am the founder of Dinner Table Math® and Trapezium Math Club,® an after-school and summer camp program for elementary students in the Philadelphia area. I also work with elementary schools to implement engaging and rigorous math in the elementary classroom. I am the mother of three children (one in middle school and two in high school) and I am thankful that I had an opportunity to positively impact their math education as young children. This blog is about what I’ve learned about elementary math in my years working with students and teachers.

#dinnertablemath #math #strugglinginmath #elementarymath #mathteaching #mathteachers #homeschooling

Why so many students struggle with math after leaving elementary school

amciver@trapeziummath.com (Angela McIver) — Fri, 30 Nov 2018 18:33:23 GMT

I set out to develop a math program for elementary students that challenged them beyond expectations, with lessons and activities that make students want to learn more.

I completed my PhD at the University of Pennsylvania's Graduate School of Education. My dissertation Understanding the Numerical Reasoning of Middle School Students focused on understanding why so many students struggle with math after leaving elementary school. What I learned from interviewing 40 middle school students (20 at the end of their sixth grade year and 20 at the end of their 8th grade year) fundamentally changed the way I think about teaching and learning.

After graduate school, I continued interviewing hundreds of students across the country (from elementary school to college) about their understanding of basic math concepts. These interviews led me to the conclusion that few students are provided the appropriate curriculum or rigor necessary to develop strong math foundations in elementary school; and when they are, their experiences are neither engaging nor confidence-building. I set out to develop a math program for elementary students that challenged them beyond expectations, with lessons and activities that make students want to learn more.

Dinner Table Math grew out of my business Trapezium Math Club. I started Trapezium Math Club because I knew that elementary students were capable of doing far more challenging math than elementary math programs were asking of them. Our math games and activities are the result of years of testing with Trapezium Math Club students and students in schools where Trapezium has a partnership. They represent many hours of debriefing with teachers about successful and unsuccessful lessons; the redesign of lessons and materials to address unforeseen challenges experienced by students; and the need to maintain rigor while moving away from the worksheet driven classroom.

With Dinner Table Math my goal is to empower parents to build strong and confident math learners at home with activities that we know work with children.

#dinnetablemath #math #learning #strugglingstudents #elementarymath

You Can Teach Your Children Math! (Especially your daughters)

amciver@trapeziummath.com (Angela McIver) — Fri, 16 Nov 2018 18:38:09 GMT

I started Dinner Table Math as a way to empower parents to build strong confident math learners at home.

After studying how children learn math (I got my PhD in this field), I've come to the conclusion that the elementary school curriculum does not provide the necessary foundation for success in middle school math and beyond.

When I interview successful math students (those who are prepared to take the most rigorous math courses in high school), I have found that most have either participated in after-school math programs or tutoring while in elementary school or, they had parents who spent time teaching them math at the dinner table (or in the car, or at bedtime, or while walking to school.....).

Recently, an article by Dr. Barbara Oakley in the New York Times, Make your daughter practice math. She'll thank you later validated my belief that parents are key to building strong math students - particularly girls. Dr. Oakley - an engineering professor- is the author of the book Learning how to learn, and helps students learn to build the tenacity necessary for doing hard math.

My goal is to empower every parent to support their children's math development in as little as 10 minutes a day.

Check out our Dinner Table Math Hacks for fun ideas that can be implemented at the dinner table and believe in your power to succeed!

#KidsdoDinnerTableMath #dinnertablemath #math #mathproblems #mathchallenge #mathgames