In our newly released Smart Bundle: Blending Middle School Math, we dive into just how important the middle grades are to future success in mathematics. Algebra can be a turning point for many in their math education. As a gatekeeper subject, it indicates future success and acts as a gateway into advanced math. We continue to see more and more resources developed to better teach and prepare for Algebra. Even companies, such as DreamBox Learning and MIND Research Institute, who have traditionally worked in the elementary space are now putting energy into middle grade expansion and Algebra. With only 30% of the US student population proficient in Algebra, we know that there is work to be done.

So how do we make sure that Algebra attracts students to advanced mathematics courses rather than repells them away? Here are 5 things worth thinking about when it comes to finding the best solutions for learning and practicing algebra.

1. Focus on relationships. At the heart of Algebra is not just “letters,” or as we prefer to call them variables, but RELATIONSHIPS. The variables are really only around to support the expression of these relationships and turn situations into written equations that can easily be manipulated and solved. The bonus here is that students tend to have built more of a schema around relationships than they have variables, so go with it. Start with the relationships and then lead into how and why variables can be used to simplify the process.
2. Think situations, NOT word problems. There is a reason that kids hate word problems…they mean NOTHING to them. Do you dread the question: when will I ever use this in the real world? You shouldn’t! There are TONS of great answers to that question, just don’t answer with word problems – The key is putting kids in situations where using algebra simplifies the problem solving process. Situations that matter to your students. Think financing, construction, cooking…the list goes on. Need some inspiration, check out Get the Math or Discovery Education for ideas.
3. Provide opportunities for productive failure and think growth mindset. I recently read an article that pointed that the solution to creating a better learning environment for Algebra was to make it an elective…in other words, make it optional. I am going to DISAGREE. Algebra is important and when presented in the right way (with the right amount of patience), it is something that ALL students can be successful in. We need to help our students understand that hard work and dedication lead to improved results. As Sal Kahn recently wrote about in his blog post The Learning Myth: Why I’ll Never Tell My Son He’s Smart, “our intelligence is not fixed: and the best way that we can grow our intelligence is to embrace tasks where we might struggle and fail.” What better class to struggle and fail in than Algebra!
4. Start Early. As we discussed with Tim Hudson from DreamBox Learning in our Middle School Math Chat: Connections are Key, Algebraic Reasoning doesn’t have to wait until middle/high school, it should actually start much earlier. Why not have your older students help develop ideas for how to teach important concepts early on? Even better bring them into elementary classrooms and let them take the lead, there is no better way to prove genuine understanding than to teach it to someone else. What makes this task even more difficult is that they have to make strong connections to elementary level math so that the younger students will be able to understand it.
5. Present Difficult problems. Don’t shy away from the tough stuff. Motivation can come from a variety of places, but when students learn what it feels like to solve really tough problems, they develop an intrinsic motivation that helps create persistence and grit.

### Resources for the Blended Algebra Classroom:

Digital Courses

• AgileMind – Online curriculum that is designed for next-gen standards and 21st century skills and puts the teachers at the heart of instructional leadership. An example of content that started as supplemental, but is now being greatly imcorporated into core instruction.
• ALEKS – Assessment and LEarning in Knowledge Spaces from McGraw Hill is a popular web-based option for High Schools looking for a full course. The program uses adaptive questioning to identify student knowledge and provide suggested courses of action to assure students progress on the pathway that works best for them.
• ApexLearning.com: For the last decade, ApexLearning has been a leader in the blended learning solution space. Includes Algebra 1 and 2 courses.
• Carnegie Learning – Carnegie Learning offers both traditional and Integrated Pathways for HS math students. Research-based and designed for the CCSS as well as the Standards for Mathematical Practice. Spanish and customizable RTI modules also available.
• CompassLearning.com – Credit recovery and course options are designed to create personalized experience for students by providing rigor and accountability.

### Supplemental Resources (incorporated into or combined with core instruction):

• CK12 – CK 12 supports personalized learning environments by providing free access to open source content and tech tools that allow for teachers to create a customizable and multi-modal educational experience for their students. Check out FlexMath for algebra resources.
• Khan Academy – Teachers can align the Khan lessons to the class scope & sequence, or simply allow students to progress at their own level.
• Gooru – Gooru is an open source and free, personalized learning solution that helps teachers organize content and connect with peers. Teachers can choose from millions of online learning content(including video and test questions)
• LearnBop – This automated system for grades 5–9 mathematics simulates a one-to-one tutoring experience by guiding students through problems step-by-step so they can learn fundamental math concepts at their own pace. Recently partnered with Fuel Education to support a focus to help kids be successful with algebra.
• LearnZillion – LearnZillion is a constantly evolving library of digital resources that designed by expert teachers that allign to the CCSS.
• NROCmath.org – The NROC project is focused on college and career readiness and has created a series of online courses to support the online learning needs of today’s students.
• TenMarks – Preloaded curriculum with content for grades 1 – Algebra 2 & Geometry, provides built in instruction with instructional videos and hints, accessible through mobile browsers, and ability to track student progress. Teachers are able to use program to reinforce their own instruction and personalize the learning experience for kids.
• Think Through Math – TMT is a supplemental, web-based program that focuses on algebra progressions and building persistence. Designed for grades 3 – Algebra 1.

### Apps + Practice Tools:

• Algebra Nation –  This study tool developed by the University of Florida takes best practices from teachers around the state to provide one resources to students, available online and on mobile devices through apps.
• ASSISTments – A system designed to give students immediate feedback and provide teachers with instant reporting that can drive instruction.
• DragonBox – DragonBox has two apps one for ages 5+ and one for 12+, allowing young students to dive into an introduction to algebra concepts and encouraging older students to further develop basic algebra skills. Voted world’s best serious game at the International Mobile Gaming Awards(IMGA).
• Front Row – Front Row is a differentiated math app for the iPad. It includes a teacher dashboard to help educators make the most of the individualized practice and content covers K – 8 Common Core State Standards.
• IXL Learning – IXL believes that “practice makes perfect” and the program is designed to motivate students through interactive games and exercises while making sure that resources are available to assure that teachers and parents stay informed and involved. Also available from IXL is Quia Web, tools to create, customize, and share their curricula online and Quia Books, Web-based versions of workbooks and textbooks and are produced with a variety of partner publishers.
• Solving the Unknown with Algebra: Developed by The Actuarial Foundation with Scholastic, this program provides skill-building activities that use mathematics for real purposes, while motivating students to achieve success in the classroom and in real-world situations outside of school.

Do you have additional ideas for what works for teaching Algebra? Share in the comment section below, or respond via Twitter using #SmartMath #Algebra

DreamBox, Fuel Education, MIND Research Institute and Scholastic are Getting Smart Advocacy Partners and LearnZillion is a Learn Capital portfolio company where Tom Vander Ark is a partner.

#### 1 COMMENT

1. With 33 years of teaching math, one critical reason this country lags behind is that teaching students to regurgitate information without connecting the concepts is meaningless. Algebra is not the sole gate keeper subject in math. If a student does not understand the concrete level of a concept they cannot abstract the concept. If you do not know that 4+5 leads to 9 then x+5=9 has no meaning. The property of commutative is recorded as A+B=B+A and the point is often missed without an analogy. The issue is about whether order under an action matters or not. Putting on your hat & coat VS putting on your shoes & socks clarifies the issue. The hat & coat scenario is order free whereas the socks & shoes action is very order dependent. The abstraction of this is that addition & multiplication enjoy the freedom of order while subtraction & division do not for they are order sensitive.
Here is my philosophy.

Formula regurgitation
Explains why this nation
Is mathematically deficient
A child learns what they need
To temporarily succeed
Passing the test seems sufficient.

Somehow mathematics
Moves to the attics
Of many people’s intellects
In boxes separated
By walls corrugated
Soon the dust collects.

However it is my belief
This achievement is brief
It feeds the mind for a short time
To never accept
Any empty concept
Is the purpose for my rhyme.

When the commutative property
Is seen as A+B=B+A expressly
It is unclear that order is the issue
Like putting on your hat and coat
Is immaterial to you.

So too, in a multiplication kingdom
But some actions have order issues
When considering subtraction
Or the division action
These put on socks and shoes.

When taught to memorize
Math fails to mesmerize
Giving the answer for a day
If shown the connections
With its’ true directions
One can solve come what may.

Thanks for reading my insights. Jo