The Goal of Math Classrooms

The goal of modern day math classrooms is to equip students to solve everyday math problems.

There are lots of approaches to developing problem solving skills. But without a foundation of numeracy, students won’t be able to reach their full problem-solving potential. Good problem solving is dependent on core numeracy skills.

Numerical Fluency

In some ways, numerical fluency is like reading fluency. Both are building blocks. Reading fluency – being able to decode words – impacts reading comprehension. Many language arts teachers have observed that students with poor phonetic decoding and sight word recognition skills read so slowly that they are unable to understand the very sentence they just read.

Poor numerical fluency has the same negative effect in mathematics. When the child’s numerical ability is lacking, they struggle to solve multi-part math problems. Numerical fluency is the ability to work fluidly with numbers in a variety of mathematical situations. Kids competent with numeracy have the ability to hold a multi-part problem in their working memory, use their skills to resolve each part, and solve the problem as a whole.

Problem Solving Example

Numerate students are capable of solving multi-step math problems – and importantly – evaluating the reasonableness of the solution. For example:

Joseph saves pictures in a 4 page photo album. He has 102 pictures in the album – 28 pictures on the first page, and 23 pictures on each of the last two pages. How many pictures are on the second page of Joseph’s photo album?

The numeracy math skills needed to solve this problem are:

The ability to double (or multiply by 2) – 23 x 2 = 46
Summing two two-digit numbers with carrying: 46 + 28 = 74
Subtracting with regrouping: 102 – 74 = 28
Evaluating the reasonableness of the solution (adding them all together to verify they sum to 102).

If your students struggle with one of these skills, they’ll be incapable – or extremely slow – to solve the problem as a whole. Most tests these days are timed – so speed matters.

Reinforcing Core Numeracy Skills

So what’s a school to do? Be sure to put a little time into reinforcing the core numeracy skills that your students will need to draw upon to solve the problems they tackle in class. A little investment in numeracy goes a long way.

Importance of Measurement in Learning

Measurement is prevalent in the classroom. Unfortunately, the feedback can take a long time for students to receive. It can take time before a paper is returned, a test is graded, or your average grade for the quarter is given which can make the clear measure of progress a little fuzzy. What we can learn from the games we play is that the faster the feedback, the easier it is to attribute that feedback to a behavior.

Learning from Games
Formative Loop is a daily math practice. Each day we see our students getting feedback as to whether they have passed to the next level. This in itself is a reward, and students are driven by it!

Points System

Learning from games, we have added a new points system to Formative Loop. This system gives students points for practicing their math skills (5 points) and even more for making progress (10 points when they master a skill). Each day, students will see their total points earned on the top of their practice paper.

Reward System
Educators then build real-world reward programs off of these points. Having a large array of options is beneficial to the students. Here’s some typical items in the reward system:

100 points – large reward (trip to the treasure box, lunch with the teacher, Hershey kiss from the principal)
50 points – medium reward (line leader, shoes off day, bring a toy from home)
25 points – small reward (get a sticker, choose the story to be read, choose your seat)

Points for Effort

You may ask why we give points even when students don’t master a skill. The reason is, we want the students to feel encouragement even for trying. This is a daily practice, not the final exam. The more engaged in practice our students are, the better the overall outcome will be.

You can also print out copies of our currency template if you want the students to practice with printed money they earn from their points.

Download Formative Loopers Currency Template](/content/wp-content/uploads/Loopers.pdf)

Practices for Success with Formative Loop

The following are the most important practices to follow for success with Formative Loop.

Commitment to Practice

Make a school wide commitment to how often you plan to run the program. We recommend 4-5 days a week. The best results come from running the program daily. Weekly reporting will help you track progress. It is important that the teachers and administration all support each other in this commitment.

Intervention Plan

When students don’t pass a skill after 3 attempts, we highlight that student as being stuck. It is important that you have an intervention plan so that these students are getting extra help to move forward.

Grading for Accuracy

Some teachers will spend time checking the accuracy of every single problem. This causes them to spend too much time on what is intended to be a daily practice. We encourage spot-checking vs. checking every single problem. It has the same benefits with a lot less time.

Incentive Program

Formative Loop will automatically print out award certificates for each student when they pass a major unit and track points as they practice and make progress. Students are much more engaged as they see recognition for progress. Building an incentive program is an easy way to get students begging to practice their math skills! Read more about Formative Loop Points.

Additional Resources

Be sure to view our getting started videos to learn more about the program.

Powerpoint Training for your school](/content/wp-content/uploads/Training-others-on-Formative-Loop.pptx)
Formative Loop Guide](/content/wp-content/uploads/Formative-Loop-Guide.pdf)

Learning Single Digit Math Facts

Kids learn single digit addition and multiplication facts quickly. They are helped by the commutative property of mathematics (2 + 3 = 3 + 2 and 4 x 5 = 5 x 4). If the addition or multiplication of 1’s (1 + 3 or 4 x 1) are not counted, there are only 36 discrete single digit addition and multiplication facts to learn.

Not true with subtraction facts: 8 – 5 = 3 and 8 – 3 = 5 appear as two separate subtraction facts. They are to a young student in the same fact family, but students must learn both of these subtraction facts. There is no commutative property of subtraction. To complicate matters, students must also learn double digit subtraction facts subtracting a single digit (13 – 8 = 5 and 13 – 5 = 8). Ask any elementary math teacher – the vast majority will agree. Subtraction facts are kids’ main adversary.

Method for Learning Subtraction Facts

Is there a method to help kids to quickly learn many of their subtraction facts? Yes. There is! Students still need to learn single digit from single digit subtraction facts (5 – 3 = 2 and 9 – 6 = 3), but those facts are much easier than single digit numbers subtracted from a double digit number (i.e. 17 – 9 = 8). There is a method that is very helpful in the latter case and adds numeracy skills of number sense and base 10 mathematics at the same time. This subtraction technique relies on student proficiency of the addition of two single digit numbers – a skill that is typically mastered well before working on subtraction facts.

This method is shown below using the math fact 15 – 7 = 8 with a typical subtraction fact format.

This method may appear complicated, but it has merit. After students are able to ‘Make 10’ quickly, they become very adept at the process – and subtraction facts are quickly mastered. The math skill of ‘Making 10’ should be taught to mastery prior to using this subtraction technique. Skill practice sheets for ‘Making 10’ are available in the Formative Loop Numeracy Resources Library.

Teachers should show the process on a number line so kids visually understand the physical nature of the mathematics and why this process ONLY works when subtracting a 1 digit number from a 2 digit number.

New Feature: Achievement Certificates

We wanted to make you all aware of a new feature we released this week: Achievement Certificates. When a student progresses through a skill level, we will automatically include a printed certificate you can use to recognize their achievement. Some teachers may want to hold these to present them all at once at an assembly, or feel free to hand them out the day the student receives the award.

Here’s an example of the new certificates:

When the feature is enabled, you will also find a new menu item under Manage Students -> View Achievements. This will allow you to create a certificate at any time.

We hope your students are motivated by the new feature! Please share any feedback you have!