Math anxiety is real. And many elementary teachers experience it. Big time.

Teachers are not only stressed about the content their teaching, but the timeline they’re held to for teaching it.

Most elementary teachers are underprepared to teach math. Even those who like doing math haven’t had sufficient training to teach math. Especially not Common Core math.

All of this can lead to low morale and teacher burn out. And that’s bad. But there are a few things teachers can get excited about when it comes to teaching math nowadays.

The following are a few points I like to hit with teachers during my professional development workshops:

## 1. Efficiency Is Less Important Than It Used To Be

Not too long ago, the “best” elementary math students were the ones who could solve problems quickly and had their facts memorized. These little calculators were praised and identified as smart – until middle school. Studies show that that’s when students who have been memorizing their way through math hit a wall. The fixed mindset they’ve developed affects their math and their self-esteem.

### These days, however, conceptual understanding is king.

Efficiency does not equal understanding or mastery. The Common Core says that fact fluency should not come at the expense of understanding. Plenty of research shows that timed tests are actually detrimental to students’ future math success.

As we follow students through the grades, we can see that those students who have strong conceptual understanding (read What Is Conceptual Understanding?) and work harder to learn math continue to persevere and do well throughout upper grades.

Many teachers become frustrated when students solve math problems inefficiently.

### This is one stressor teachers can let go.

Allowing students to work longer on fewer problems

- allows students to take ownership of their solution,
- provides the teacher with lots of information about how each student is thinking, and
- helps teachers pinpoint where misunderstandings are occurring in the problem solving process.

### Instead of judging students’ math ability on speed, teachers can create clear grading guidelines that will make life easier for themselves, the students, and parents.

If a student can regularly solve a problem with 2 different strategies (no matter how efficiently), she gets a “4” or “A” for that skill.

If a student can regularly solve a problem with 1 strategy (no matter how efficiently), she gets a “3” or “B” for that skill.

If a student can show work and is on the right track to solving a problem with 1 strategy (no matter how efficiently), but cannot regularly find the accurate solution, she gets a “2” or “C” for that skill.

If a student does not show work or uses the wrong operations to solve a problem, she gets a “1” or “D” for that skill.

You will be amazed how this grading scale affects students’ math work!

Students who are encouraged to solve problems with 2 strategies catch their own mistakes and create incredible math connections.

Providing less work and more time for problem solving, efficient or not, will help teachers and students enjoy math class.

## 2. Interleaving Helps Teachers Get Through Their Curriculum

Something I hear from teachers all the time is that they can’t get through their curriculum in a school year. Definitely not with time for review before end-of-grade standardized tests.

When I ask teachers what the problem is, they often have one of two (or both) issues:

- they wait for mastery of one concept before moving onto the next, or
- behavior problems in the classroom slow down teaching.

### Interleaving is here to save the day! What is it, you ask?

Interleaved practice is when students practice one concept and then another and then another, and then finally come back to practice the first again. They problem solve and learn in an ABCABCABC format.

“Blocking” is the opposite, where students practice the same concept over and over again. Blocking is the most common way we try to teach students, but it is far less effective. Blocking is when students practice AAA before BBB before CCC.

### What’s crazy is that most textbooks are organized by blocked units.

(Scientific American has a great article about interleaving if you want to read more and see some statistics.)

There are a few theories as to why interleaving works so much better than blocking.

Spacing: Memory researchers have found that deeper learning takes place when students have breaks, or space, between practice. If students are introduced to adding fractions on Tuesday, their understanding will actually grow in they practice a different math skill Wednesday and then return to adding fractions later that week.

Discrimination: Our brains are great at picking out differences. When students add and then multiply and then subtract, their brains have a chance to find all the similarities and differences between those operations.

Retrieval: When students participate in blocking, or learning one unit at a time, they are able to keep information in their short term memory. They might appear to be doing well during the unit, but forget much of what they knew by the end of the school year. With interleaving, students’ brains are constantly asked to retrieve information needed to solve problems, which creates strong and lasting memory pathways.

### Interleaving leads to better class engagement and helps students master concepts with less practice!

In fact, teachers *should* move on from one concept to the next before most students have a chance to master the first. When the concept is revisited later, the class will make greater gains in the area *because of the break from it*. Isn’t that fascinating?!

Get interleaved stations here.

## 3. Exploration Is One Of The Most Effective Ways For Students To Learn, And It’s Easy On The Teacher

What’s the best way to help students develop seamless understanding? Give them time and tools to build knowledge on their own.

If you want an engaged class of motivated learners, set up stations where they work together or independently to solve problems without teacher help. Kids feel the respect from teachers who let them hash out problems with their own unique strategies.

### Teachers understand how powerful exploration is when they participate in activities at my professional development workshops. In less than 10 minutes of solving large division problems with base 10 blocks, I always hear exclamations from teachers who never truly understood the concepts behind long division.

### Teaching through exploration first saves teachers so. much. time.

The best part is, the problem solving strategies that students come up with are based on the math they know and the ways of solving problems they’re comfortable with.

### When we show students a strategy for solving a problem without providing lots of exploration time first, we are creating learning gaps for most students. If I show you my way of multiplying 2 digit numbers before I’ve let you create your own, you’re…

a) missing out on authentic problem solving practice,

b) focused partly on the context and partly on trying to think like me,

c) learning a procedure and not the concept, and

d) less motivated by the efficiency of my strategy because you haven’t had time to create your own inefficient one first.

Some teachers may fear that “Exploration” is some free for all time where students may or may not learn something. This is certainly not what I’m pushing for.

Exploration activities should be thoughtful and well planned. Here is an example of an exploration with pattern blocks that helps students build area, multiplication, proportional reasoning, and ratio skills.

### Through exploration activities, teachers spend less time (if any!) in front of the class, and more time circulating, listening to math discussion, supporting struggling students, and taking informal assessment notes.

Exploration activities are fun for everyone. Including the teacher.

This set of math stations includes two exploration activities: a multiplication exploration with base 10 blocks, and a challenge for students to create word problems for given equations.

## 4. Math Talk and Math Discussions Lead To Better Understanding, And Make Use Of Teachers’ Language Arts Skills

Did you know that most elementary teachers have a language arts background and/or preference?

Because of this, many elementary teachers are uncomfortable teaching math.

The good news is, hosting a discussion about math everyday will dramatically deepen students’ understanding of the concepts and strategies they’re learning.

Just like you would lead a discussion about a novel, you can ask students what connections they made, what patterns they noticed, and how the math made them feel.

### Using the last 10 minutes of class to discuss the day’s math is well worth the time. It isn’t lost teaching time, it’s extra effective teaching time.