Tales from the classroom

“Summer Math” Suggestions to Boost Student Understanding

June 23, 2016 by Beth Curran 4 Comments

School is out and summer is calling, but for many teachers and administrators, summer is a time to take stock and plan and budget for next year.

As a teacher, this is a glorious time of year, but also one of worry. I worry about my students. I worry about those who needed extra support throughout the year understanding and retaining math concepts. How will they fare next school year? Will they regress over the summer months if they don’t do any math work?

There are three categories of students who benefit most from summer math work:

Those who have struggled all year and maybe never quite achieved mastery on those critical grade level concepts,
those who easily forget concepts, and
those whose math confidence could use a boost.

With a Singapore Math program, there aren’t many ready-made options to pick up at the local bookstore. Books that are available focus heavily on procedural understanding rather than underlying math concepts. So what’s a teacher to do?

Aside from recommending tutoring, I have found a couple of options that seem to meet my needs as a teacher and the needs of my students.

Workbook Work

For those looking for a paper and pencil option, I recommend the Extra Practice books from Singapore Math’s Primary Mathematics series. Students should work at the grade level just completed (a rising 3rd-grade student should do summer work in the 2^nd grade Extra Practice book).

The Extra Practice books offer parents and/or tutors “Friendly Notes” at the beginning of each unit that explain how to re-teach concepts in a way that is familiar to the student. The notes are followed by practice pages that give parents sample problems appropriate for practicing the concepts and the student an option of working through problems independently. Best of all, they include an answer key in the back so parents can check work and students can re-work problems, if necessary.

These books are written to cover a year’s worth of concepts; I am by no means suggesting that a child complete the entire book over the summer. Teachers recommending this book will need to tailor the tasks to meet each student’s needs. This can be as simple as highlighting the contents page to include units or pages that you would like the student to complete over the summer keeping those critical concepts in mind.

Another option for summer work can be found in online programs. I have come across three online options for concept practice; Primary Math Digital, it’s twin Math Buddies and a program new to the US market, Matholia.

Online Options

Primary Math Digital (Free 15-day trial) and Math Buddies (Also a free trial) are backed by Singapore Math’s Primary Mathematics and Math in Focus series. Both offer students video tutorials that can be viewed by the student (and parent) an unlimited number of times. These videos are scaffolded to follow the pictorial and abstract progression of learning.

Teachers can assign videos, practice and assessment tasks f $Math Buddies$ or students to complete over the summer at their own pace. The practice pages can be a little challenging to navigate, but with some initial guidance, students should be able to complete the tasks independently.

Both programs require the school to purchase annual student and/or teacher accounts to gain access to the library of lessons. There are Homeschool accounts available. Expect a price tag of around $30 per student depending on the number of accounts purchased.

Another, more affordable option new to the US market is Matholia. Matholia was developed by two teachers from Singapore and has been used by teachers and students in Singapore as well as several other countries. This program also includes a library of video tutorials, practice and assessment tasks as well as fact fluency tasks and games.

The videos are easy to understand and are also strategically scaffolded for student understanding. The practice and assessment tasks are intuitive and easy for students to navigate. As with the other programs, teachers can assign tasks for students to complete over the summer.

Matholia also requires the school to purchase annual student accounts (teacher accounts are free) but is much more affordable at just $8 per student.

Don’t forget the concrete…

I can’t go without saying that any of these options will give students practice, but struggling students need more than just extra practice working through math problems. They need more time in the concrete phase of learning using manipulatives; base-ten blocks, place value chips, model building with connecting cubes or paper strips, fraction strips or circles, etc. So, please, consider not only sending these students home with books and login IDs but also with a bag of manipulatives for hands-on learning and practice.

Now…back to dreams of lazy mornings and time to relax and recharge. Have a great summer and rest assured that your students will be prepared for the next grade with a little summer math work.

Filed Under: Math Resources, Tales from the classroom Tagged With: materials, Singapore Math resources, tales from the classroom

Great Math News from City Springs School In Baltimore

May 24, 2016 by Cassy Turner Leave a Comment

For the last year, I’ve been working with City Springs Elementary/Middle School in Baltimore. Here’s a short description from the school’s website:

City Springs Elementary/Middle School is a neighborhood charter school operated by the Baltimore Curriculum Project (BCP). We are a conversion charter school, which means we were an already existing Baltimore City Public School that was taken over by an outside operator to bring innovative and research-based curriculum and other programs to enhance the school. To learn more about BCP, click here.

Initially, the school was seeking help with its Middle School math. After I made a pair of on-site visits at the end of the 2014-2015 school year, Dr. Rhonda Richetta, Principal of City Springs, decided to adopt Singapore’s Primary Mathematics Common Core Edition.

I’ve returned to City Springs periodically this year to provide continuing support as the school’s teachers and coaches adopted a Singapore Math® curriculum. The school is making remarkable progress, and I want to share stories written by some of City Springs’ dedicated teachers about the students’ growth during the year.

I’ve clipped an excerpt from each story with teachers’ observations and very valuable insights about the program and why it is working so well for their students. Please click on the links to read complete stories from the school’s website. I love the photos of students showing off their skills and having fun with math!

Ms. Schoenleber: Introducing Singapore Math (November 2015) “Classroom manipulatives have helped our kids get better at problem solving and justifying their answers for tough math problems.”

Ms. Hagemann: It’s More than Just a Game (November 2015) “One way to get stronger in mental math is by use math-based games to reinforce basic concepts and encourage mathematical thinking…Students in Ms. Hageman’s class love mental math games!”

Ms. Smith: Moving Ahead in Mathh (February 2016) “Singapore Math has been very challenging but it has also been very rewarding, and they have especially loved the use of manipulatives in class.”

Ms. Barry: Stepping Up to the Ratio Challenge (February 2016) “Ratio problems can be really tricky. Sometimes these multi-step problems are so challenging that we spend 15, 30, or even 45 minutes on one problem! Our students love to rise to the challenge, and have grown so much in their math skills with these complex problems.”

Ms. Barry’s also class wanted to challenge readers to solve a ratio problem they worked on. How did you do?

Ms. Lineberry: Introducing Fractions (May 2016) “At first, we struggled to figure fractions out. Trying to wrap our minds around halves and fourths proved difficult at first. Things became a little clearer after we started using “manipulatives,” hands-on objects used to illustrate math concepts.”

Ms. Williams: Knowing All the Angles (May 2016) “Students began their geometrical journey by learning how to measure angles…Later, they will start learning to measure geometric angles made by two lines emanating out of the center of a circle, and eventually beginning exploring the complex world of geometry formulas.”

Working with City Springs has been one of the most rewarding and enjoyable assignments of my career. Teachers have embraced the challenge of adopting a new program and students are making wonderful progress. I can’t wait to see their growth in Year Two! Thank You, City Springs!

[Full disclosure: My work assignment at City Springs is contracted through Staff Development for Educators.]

Filed Under: Math Resources, News, Schools, Tales from the classroom, Training Tagged With: adopting Singapore math materials, School News, Singapore Math curriculum, Singapore Math training, tales from the classroom

How can I fit it all in?

May 19, 2016 by Beth Curran Leave a Comment

In 2015, Beth wrote about the Primary Mathematics adoption process at St. Anne’s-Belfield School. Here’s an update on the school’s progress.

As the year winds down and I look back at all that my students have learned this past year, I still feel panicked at what’s left to be covered. This is the end of a 3-year adoption cycle of Primary Mathematics and while I’ve been able to cover more curriculum than in the previous 2 years, I am still left wondering, “How can I fit it all in?”

In the fall of 2013, we adopted the Primary Mathematics curriculum in Kindergarten through sixth grades. We knew this would come with its challenges but felt strongly that if we were going to offer our students the “world’s best mathematics curriculum,” then we needed to offer it to all, not just those who made the K, 1, 2 cut.

With this plan, we knew there would be time spent filling in holes in our first year, teaching skills and concepts that the students were missing, and building a solid foundation in number sense and place value. We accepted the fact that we would not cover all of the curriculum that first year, and worked with Cassy Turner to develop a sequence for each grade level that included teaching critical lessons from prior grade levels.

Year 2

In the second year, teachers were feeling a sense of relief. We’d made it through that challenging first year. We experienced the curriculum from start to finish, well – at least our version of it, and we felt confident. We weren’t faced with the need to back-teach (as much). Our students entered the year having learned and retained a deeper understanding of those critical math concepts.

With Cassy’s advice, we created a new plan for our second year. We knew the lessons that had been skipped the previous year and teachers worked together to map out a Kindergarten through sixth-grade sequence that allowed us to get further through the content, and more importantly, accounted for previously omitted lessons. If we didn’t teach a lesson on geometry to our third graders our first year, we made sure those students would get those lessons in fourth grade our second year.

The year ended, and our standardized test scores showed slight increases in problem solving and algebra readiness, both areas of statistical concern with our previous curriculum.

Year 3

Entering year three, we felt confident in our abilities to deliver lessons. Along with our students, our staff had developed a deeper, conceptual understanding of math. We were able to effortlessly explain new concepts, differentiate on the fly, and anticipate misconceptions. We incorporated anchor tasks, journaling and finally had a grasp on how to effectively use all of the materials.

We entered the year with the goal of teaching the entire curriculum. Halfway through the year we were teaching material nearly a month ahead of our previous two years and felt really good about it. Then came…

rehearsals for performances
grandparents’ day presentations
spring field trips…
field day…
and all sorts of other school commitments.

By April, we had just about lost the scheduling lead that we had enjoyed in December.

So, here I find myself once again faced with the task of choosing one lesson over another and prioritizing the importance of skills and concepts that I may or may not have the time to teach. Fortunately, the list to choose from is smaller than in the years before. I’ve been able to cover almost all of the material, nearly reaching the goal.

I consider myself lucky to have been in a situation of specializing in math in the lower grades over the past 3 years. I have been able to experience the strengths of the sequence, which in my mind, is one of the pillars of success of a Singapore Math curriculum. Going forward, I know it will be easier to thoughtfully prioritize content to eliminate the risk of creating gaps or holes in student learning that could potentially weaken their foundation.

As I leave the school, I look forward to bringing this wealth of knowledge that I gained over the past 3 years to Math Champions and look forward to assisting other schools that are facing the question of, “How can I fit it all in?”

Filed Under: Implementing Singapore Math, Math Resources, Tales from the classroom, Training Tagged With: Singapore Math training, tales from the classroom

Bar Model Solutions – by Students

April 12, 2016 by Cassy Turner 2 Comments

After the post on Assessing Bar Model Solutions went up, Beth Curran sent a message: “We just did that problem!” She agreed to share some student work:

And when the students didn’t draw a model:

I see this as a comparison problem:

5 units -> 125 students
1 unit -> 125 ÷ 5 = 25
7 units for boys -> 7 x 25 = 175 boys in all

(That’s the Thinking Blocks Model Drawing tool that allows you to insert your own word problems and solve – or you can use the pre-made questions!)

Filed Under: Math Resources, Tales from the classroom Tagged With: Model Method, Singapore Math word problems, tales from the classroom, Word Problem

Assessing Bar Model Solutions

April 12, 2016 by Cassy Turner 6 Comments

It’s important in a Singapore style program for students to understand bar model drawing as a tool to help visualize relationships between the known and unknown in a word problem. It helps students see the algebraic structure in problems in a more concrete manner. Developed by a Primary Mathematics Project team of the Curriculum Development Institute of Singapore in the 1980’s, the Model Method for problem solving (as it’s known in Singapore) was designed as a pictorial stage to help students learn abstract mathematics.

The model method has been incorporated into the Progressions documents for the Common Core State Standards for Math (CCSSM) as a “tape diagram”. The CCSSM glossary defines a tape diagram as:

“A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.”

As such, bar models are becoming ubiquitous in elementary schools. Books have been written about Singapore’s model method, my favorite being The Singapore Model Method for Learning Mathematics:

There’s plenty to be covered with bar models, and I thought I’d share answers to the most commonly asked questions I get from teachers on model drawing:

How do you get kids to draw models when they already know the math?
How do you assess them?

When models are introduced in Singapore textbooks, the problems are very simple and students will typically know what operation to use. The first part whole models in Primary Mathematics, Common Core Edition are in the 3A textbook:

And the first part-whole model lessons in Math in Focus are in 2A:

Those are pretty easy word problems and most kids are waving their hands, with that “I KNOW the answer” look on their faces. It’s important to reiterate to students, “I’m sure you know the answer and even the equation to get there. What we’re learning today is a new way of drawing a model for our word problem so that we can work with more challenging problems in third grade. Problems like”:

A father shares $60 among his three sons and one daughter. If the daughter gets twice the amount that each son gets, how much money does his daughter receive?

or from 4A

We’ll come back to that one.

When assessing word problems, the solution method is a significant part of the answer. Students should expect to show their work to get full credit for a problem. As a teacher, it’s important to keep in mind that there is no one-way to draw a bar model.

A word problem might consist of points for the method of solving as well as points for correct computation and answers. To encourage students to draw and become proficient with bar models, I have used a rubric for assessment:

1 point for a representative diagram – Does the model make mathematical sense?
1 point for correct labeling, including the “?” to represent what is unknown.
1 point for computation on the first step and, if more than one step…
1 point for computation on the second or more steps
1 point for a correct answer in a complete sentence

Let’s look at an example. This is a student-written two-step word problem from third grade:

Does the bar model make sense? +1 point

Are the bars labeled? Are question marks in the correct places? +1 point

Is the computation to figure out the value of one unit correct? 384 ÷ 6 = 64 +1 point

How about the computation on the second step? 64 x 5 = 320 +1 point

Is the answer in a complete sentence? +1 point

So, what’s the deal with the 64 ÷ 6 equation? A byproduct of requiring students to show their work is that oftentimes, they will leave work on the paper, just in case. As a teacher, I love that this provides me with some insight into this student’s thought process:

I’m pretty sure I know what I’m doing, but I still am a little confused.

Which is exactly what the student said when I asked her about the extra equation. She realized her answer couldn’t be right because:

I ended up with 14 remainder 4 meatballs, and how could that happen?

Without a system to evaluate, you end up with:

I’m drawing boxes because I’m supposed to… I don’t get it.

This model doesn’t make sense. The student’s computation is slightly off, but she knows she needs to add. A teacher can also see from this model that more re-teaching and practice is necessary for this student and probably others in the class.

As students progress, the rubric may change. At the end of a unit/school year, the same problem might be worth three points; one apiece for diagram, computation, solution. I often tell students, “You don’t need to draw the model if you feel you understand the problem, however, you will be graded either all correct or all incorrect. Without the models I can’t give you partial credit for your thinking.”

Most students draw them anyway as a way to check their work. Some just start to see them in their heads. Here are a couple of examples from the end of a fractions unit in 5A