Who knows better than you how you learn best? With all the different learning tools offered by Tilton's Algebra, nothing is more important than letting you decide how to use those tools to meet the unbending standard of mastery set by the unforgiving exams we call Missions.

By putting you in charge we unleash your natural creativity. When you get stuck on a Mission, you decide which tool to use to get unstuck, whether it be more practice, reviewing a video lesson, or consulting other students in the public Study Group forum. It is your call.

And, of course, you proceed at your own pace, never tackling more advanced work without mastering its prerequisites.

A good teacher helps you discover Algebra for yourself by combining common sense with a sound understanding of arithmetic.

A good teacher loves the logic of math. They help you connect key elements of simple problems to straightforward solutions using common sense. You learn you can unpuzzle more complex problems by finding and solving the simpler problems hidden within them. You, too, come to appreciate the logic of math.

At every step a good teacher gives you a wide variety of problems to solve, so you learn the essential features that call for one approach over another. They have you do as many problems as you need to master one skill before moving on to the next. They let you learn at your own pace.

As the year goes by your widening array of math skills organizes itself naturally around the meaningful connections you are forever making between the structure of a problem and its solution. You recognize even unfamiliar problems by their abstract qualities and understand how to attack them. You have learned the math.

Tilton’s lessons are not your ordinary Algebra lessons. As math gets harder, our understanding must become more rigorous, our foundation must be solid. Before addressing traditional Algebra, you will go all the way back to ideas as simple as \(1-2-3\).

You will discover zero for yourself and realize why the Romans did not have a symbol for it. You will look at fractions more closely than ever before, learning the Latin origin of numerator and denominator and how those Latin meanings explain why fractions with unlike denominators cannot be added. You will learn that fractions are about multiplication, not division, then put this all together to decide yourself whether or not \(1\over 0\) equals infinity.

You will come to understand negative numbers more rigorously than you may have in Pre-Algebra. You will learn why subtraction is awkward and how negative numbers let us avoid it. You will see that negative numbers are not simple values (\(-3^2=-9\) even though \(-3\cdot -3=9\)) then use that insight to master signed arithmetic. Later on when you learn that \(-3x\lt 15\) entails \(x\gt -5\) you will be able to explain why, not just recite the rule.

Once you begin classic Algebra, you will apply simple common sense and your rigorous foundation in arithmetic to solve the early problems. Later, when you tackle more interesting problems, you will know to look for the simpler problems hidden within them.

Finding those simpler problems may not always be easy. Doing Algebra will often feel like solving a puzzle, but you will be ready for that because early on we will have fun with a few such puzzles. We will turn \(0.\overline{9}\) into \(1\) and \({a-b}\over {b-a}\) into \(-1\), with nothing more than simple Algebra.

With a good teacher, you will feel like you invented Algebra, and in a sense, you will have.

Stuck on a step? Don’t even know where to start? Could your number facts be stronger? Tilton's Algebra helps four different ways. Ask for Socratic hints; see a similar problem solved; watch a video about that specific step of the problem; or ask the Algebra community. Tilton's Algebra offers you all that help, but never so much help that you never learn anything. We make you connect the dots so the next time you run into the same kind of problem you will have a better chance of remembering the math.

Learning requires practice, practice, practice. Quality practice means instant feedback, not feedback delivered a day or even thirty minutes later. Tilton's Algebra checks every step of every problem, not just the final answer.

Right, wrong, or headed in the wrong direction, you will know it immediately. The anxiety of doubt is eliminated and small wins get rewarded on the spot.

Mistakes tell you where to hunker down and concentrate. If the Algebra has you stumped you can get help from the system, videos, or other students all within the app. If you made a careless error...

...just fix it. Now you can tackle Algebra even if your arithmetic could be stronger or if you tend to make careless errors. Your number facts will become stronger and you will learn to slow down and check your work.

How do you know when you have learned Algebra? Test yourself! Now there are no Socratic hints, no solved examples to review, and no second chances. One mistake and the problem is marked wrong. Too many mistakes and the test is failed. To make things even tougher, every mission includes problems from earlier topics.

We call these "Missions" because they work like a video game: the "levels" do not get easier so you have to get better. You can attempt a Mission as often as you like, and even quit early if it is not going well. Failed or abandoned missions are never recorded. As long as you are seeing progress, just keep trying!

If you are not seeing progress, go back to guided practice for step-by-step help or review a video lesson to see what you missed. It is up to you.

Missions do more than test your mastery. You must pass Missions on easier Algebra skills before qualifying for more advanced Missions where those basic skills are needed for success. This keeps you from getting discouraged by tackling work that is too hard. It also defines a good learning sequence for the self-taught Algebra student, and for those who want to learn Algebra faster.

No matter how powerful we make it, Tilton's Algebra is still a computer system and can do only so much. Often it takes another person to figure out what we are missing. When that happens you can check in with our on-line community of learners and Algebra tutors.

Search the forum archives for someone asking the same question, or start an entirely new thread to get the help you need. Just click the Study Group icon while working on a problem and the software will create for you a draft post prefilled with your math problem and with tags showing the math topic at hand. Just add your specific question and hit "Send".

Strong students can participate, too, helping fellow students when they get stuck, perhaps learning something in the process: the best way to master a subject is to teach it.

As with any social site you will be able to score the help you get when you like it and follow other members of the community you think are especially helpful.