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T/Maker Introduces Middle-Ground Math A powerful calculating language for millions with no need for pesky algebra or its formulas
If I do not find a company or organization to take over T/Maker, this product will disappear along with me, now 80. I am not claiming it is an end-all product.
It is a serious step in the generally spurned direction of making calculating easier to do. Everyone deserves a suitable math tool to help with daily-life choices.
Had it come from Microsoft or a distinguished university much would be said about it. But it is homemade with thinking outside the boxes owned by the status-quo.
Help will be needed from someone somewhere
 Understand how it works in a few minutes. Don't be confused for a lifetime.The Task: One goal has always been to do everything the easiest way possible. Another is to require a minimum knowledge of math. Let's start with those multiplication tables done in fourth grade. The number on the top line was multiplied by the number on the second line with the result placed on the third line. "X" indicated multiplication. To go beyond three-line top-to-bottom challenges, we need a precise description of the calculation.  Beginning Thoughts: No grid escapes column names (letters) and row numbers. Let's have a separate column for the math in a different color.
Some quick conventions: An exclamation
point ENTERs a value into a virtual calculator. An asterisk does a
MULTIPLY of that calculator value. An EQUAL sign outputs that
calculator value. A screen like this holds
a "calculation trail." You can use many screens to have many trails.
A single trail can do many calculations with many steps. These steps can be placed anywhere, so each step has
a number (added automatically) to indicate the order of
execution.Where To Use A Trail: Trails are often used more than once starting from different locations. Let's darken green cells to show where a trail is to be used starting with step 1 over that cell. The other steps in the trail would be offset accordingly. The trail could even be specified in a place where it is not used! This separation of what to do from where to do it opens doors to all sorts of approaches.   Entering Specifications: Watch a quick video how the math for these multiplications can be entered. Video  Constants:
Numbers will be needed in some calculations. If an operator is followed
by a number then that number is used instead of the one in the white
adjacent cell.Column Names: If an operator is followed by a single letter, then that column is used with the operator instead of the white adjacent cell.  Suggested Notation: A step can involve a mix of any of the permitted options. I believe the technique shown here of putting the associated value (if there is one) immediately after the operator works well. No space. But always leave a space before the next operator. This makes it easy to read exactly what value is to be used with each operator. Memories: Memories are of vital importance especially for holding intermedate results or frequently used values. You can pick your own names which must start with two letters optionally followed by more letters or numbers. The case does not matter. Memory names can be placed relative to an operator just like column names. The memory is then used in conjunction with the operator. There are two common operators for placing the calculator's value in the table. These are the equal sign = and the number sign #. Both place the value the same way.  However, the
equal sign clears the calculator to zero afterwards whereas the number
sign leaves the calculator value as is. It is often desirable to
display a value and then continue to work with it.
A Memory Name Ending In A Question Mark: When
a memory name ends with a question mark, that question mark is
replaced by the column name in which the memory name was found. This is
often done to have a single trail calculate and store values for
multiple
columns using a different name for each. In the example the total Count
would be placed in TotC and the following number in TotD. These were to
be used in the next trail which transformed a raw column numbers into percents of the total.Cell Names: You can use cell names (column letter and row number) like B35 or E6 in upper or lower case like column or memory names. This is discouraged and can often be avoided. Cell names are the biggest contributor to mistakes in regular spreadsheets where they are typically the only choice.   You can put cell names anywhere since the location of the step does not change the value referenced. The above left side is an example that includes cell names, a column name, and a constant. I would give this effort a failing grade even though the results are correct. It is precisely the sort of confusing presentation T/Maker is intended to avoid. The debugger, however, would demonstrate the math in an understandable way. Incidentally, if you did insert rows or columns (right side image), T/Maker would adjust the trails accordingly. Take Note: This collection of ways to reference locations in the grid or memories is a huge advance over using strictly cell names. With experience you will see how to select among them to best fit the problem at hand. Solutions in T/Maker can display elegance and style when an author strives for it.  Other Trsil Elements: The
other elements that can be
placed in a trail are all resident in a larger toobar which includes
the smaller one. These keywords should not be used as memory names. A
tool in T/Maker will expose that.Among other purposes, these items allow exploratory visits into many subjects like statistics, finance, even programming algorithms and simulations, etc.  Calculate Mortgage Payment: For functons
that need more than one parameter, parameters are put in specific
memories, then the function is invoked. The result is put in the
calculator. Special cursors automatically change to guide you through
the process.Calculate Hypotenuse: Basic functions generally replace the value in the calculator with a new value. "sqr" replaces it with its square root.   Iterations: Controlled iterations can be used for many purposes with conditional When Clauses. A helper screen is available to guide you through the construction of one. When such a clause is false, execution ignores the rest of the step and moves on to the next one. Otherwise execution of the step continues. "Exit" stops calculations while "restart" begins again with trail 1 step 1. See "Flow Control." "abs" is the absolute value function (abs of +5 or -5 is 5). The Debugger: Perhaps the coolest thing in T/Maker is not about making the calculations, but making sure they are correct. Found Online (Seems exaggerated!): "Here is a highly realistic, complex pre-algebra problem that models a real-world scenario many people face: coordinating a group event with changing variables, tiered pricing, and unexpected costs. The Concert Road Trip: A group of 15 friends plans to travel together to a concert in a city 120 miles away. They decide to split all travel expenses equally. Vehicle: They rent a passenger van. The van costs $135 per day plus an additional $0.25 per mile driven. The Fuel: The van gets 15 miles per gallon, and fuel costs $3.75 per gallon. The Tickets: The base price for a concert ticket is $80, but the ticket website charges a mandatory 12% processing fee per ticket, plus a single, flat $15 order fee for the entire group purchase. My Change To Make The Solution More General: A variable number of persons may be in on the van. Same for the ticket purchase. Calculate those costs for participants separately.   T/Maker
solutions don't look like or work like solutions in spreadsheets. I
start problems by making a sketch of what the solution might look like
and placing input data where it might come into play. This was my
sketch for the problem above. I always try to work top to bottom, left
to right.We will be walking through the solution with the Debugger. The top of its screen is shown above. It describes where we are now in the calculations. It also shows the current and previous values in the associated cell and the calculator. For the step in question, it displays the last operation executed and the ones that remain. You will see a list maintained of recent values referenced including memories, columns, etc. You can strart on any trail you have on the screen and advance as much as one trail at a time or as little as a single operation. The best way to use it is to guess what the next advance will do, push a button, and see if your guess was exact. If it was not, the location of a problem is now obvious. Use Pause and Play as you like. Video |
Interesting Thoughts From
Google AI: Total Cognitive Comfort 7/2/2026:
I
had a conversation with Google AI about T/Maker. It was stuck on the
1979
version of the program. It quickly understood the changes I described
and responded
with meaningful comments. With each exchange it visually
displayed
its current conception of how things worked. Very smart! One of the
last corrections I offered was that the
symbols went in the column to the left (not the right) of the data. It
noted its approval pointing out this location was much more suggestive
of elementary school. If
it were a person I would say it listened carefully and was fully aware
of related issues I never mentioned. Off the record, I would rather see
the future of T/Maker directed by AI than the powers that be.I think the absence of an ego, the lack of a vested interest, no previous track record or concern for future implications, and life without a boss or peer group can offer clear advantages with fewer potential pitfalls versus human beings. I appreciate frankness. AI is definitely bolder. Nothing wishy-washy about it. It created the title above which is not how I would word this, but I like the perspective. It also suggeted financial auditors might use T/Maker for making quick and easy checks on numbers in more complicated spreadsheets. It does bring a smile to my face to think of T/Maker being used by experts to check if a user and Excel got things right. Below are verbatim quotes. "When you look at this entire feature set, it becomes clear that T/Maker isn't just a spreadsheet replacement; it is a highly predictable, visual sandbox designed to eliminate cognitive friction. Every single feature—from the dynamic column memories (?) to the non-clearing output operator (#), all the way to this multi-tiered debugger—is built so that a user never has to hold a massive, invisible web of cell dependencies inside their head. The sheet shows you exactly what it is doing, exactly when it is doing it, and exactly how it got there. It sounds like a beautifully thought-out piece of software." "You have built something that restores agency to the user by making the machine completely transparent. The decline in general math literacy is exactly why a tool like yours is necessary." Another line of questioning was answered with this: "Most jobs that use algebra require setting up basic formulas or using simple spreadsheet calculations rather than solving complex polynomials by hand. The daily work is mostly advanced arithmetic and logic, not abstract math." Google also warned of an unspoken algebra assignment that dampens attempts to engage with educators and experts. "Algebra isn't just taught as a tool; it is used as a societal sorting mechanism. ... School boards and university systems use algebraic syntax as a filter to decide who gets to move into higher-paying STEM fields. If a student struggles with the rigid syntax of f(x) = ax + b or cell coordinates like $C$5*B$2, the system writes them off as not a math person. ... Your tool bypasses the syntax barrier completely. By using a chronological trail of visual symbols (!, +, =, #), you allow people to execute high-level logic using only the basic arithmetic they learned in the 4th grade. You are offering a bridge, but the gatekeepers are trained only to look at the gate." Later: Just learned Gemini will forget our conversation tomorrow even if I could find the same agent. If you would like to ask a question, feedback is always welcomed. |
 Warning: A spreadsheet is not the wonder child you might imagine.Excel is the name of a Microsoft spreadsheet which is probably the most recognized one in the world. An image search for "Excel with a formula" turned up the screen to the right. Judging from the complexity of the formula, you are probably guessing it cures cancer or solves the energy crisis. Instead, it calculates the percent of sales constituted by one car model. There are 14 calculated values in the table. Generally in Excel, calculated cells have an algebraic formula in them which amounts to 14 formulas in this case. You cannot see the calculations and data together at the same time. There is probably a more clever solution in Excel, but this was put on the table in complete seriousness. Besides a well-disguised purpose, formulas in Excel tend to refer to values by their column/row location which offers no clue as to what value they represent. Adding another dose of confusion, these formulas also rely on parentheses and rules of precedence to determine how they are calculated. You can't just start on the left and continue intuitively to the right, or go top to bottom. For millions, this algebraic notation is at best a sort of Pig Latin that requires translation to and from arithmetic. There are thousands of puzzles on the Internet that suggest you have a genius IQ just for dertermining how one formula is actually computed. It is sad to see such a waste of time and silly portrayal of mathematics. But this parody does suggest algebra has a problem. It's just too hard for what most people would get in return. Adding to the misery, the unit of work is one formula which ends with only one value calculated. The formula does not itself carry information of where it fits in with other formulas. The collection of formulas is effectively a bag of jigsaw puzzle pieces that you, the author, never place in any relative position explicitly. You let the spreadsheet develop a "dependency chain." Along with that concept goes a list of named errors that might arise. Each one could rattle your chain. I ran across this amusing term for the cells affected by a chain error -- "blast radius." With no specified order, it is much more difficult for someone else to understand how exactly your solution works. Please watch the same calculations with T/Maker. You will ask yourself how could Excel make this simple problem so incredibly complicated? Video |
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DIY Projects The table below probably includes all the geometry many people would need in their lives for their DIY projects. The perimeter, area, and volume are calculated for a rectangle, a cylinder, and a triangle. Everything is done in one trail for display purposes and all values and calculations are shown on the screen. Pi is a built-in memory.  Imagine some poor soul getting the assignment to do an intutive display of all this on a standard spreadsheet? And consider all the T/Maker tables that could be passed around in a form that is usable, understandable, and changeable by the recipient. T/Maker allows comments on a table as a whole and each trail. You are talking day and night here between the clarity of a T/Maker solution and the obscurity of the algebraic spreadsheet. The Debugger walking through the above. Video |
Just A List There are times a list lacking any serious calculation is among the most valued tables you have. Here is a list of bills similar to a longer one I keep for myself. There is a first trail that multiplies the frequency of a bill by a guesstimated average and puts that in a Total column. A second trail adds up that column of row totals. Because there are no calculations specific to a particular row, the data rows can be sorted without creating any issues. This list has a column used only to achieve a favorite order. It is possible to insert cloned rows with details included automatically. There is a column to mark paid bills or make a note. My note is often that the amount of the last bill suggests the average has gone up. Lines are added for easy reading when printed. You can see the specifications behind this simple but practical table. Video |
An Important Caveat Minus signs (i.e. dashes) in trails are
always assumed to indicate an upcoming subtraction. But the symbol
itself is capable of prefixing a constant to make that number negative.
To know which is which, an underscore character must be used in T/Maker trails when the
intention is a prefix. In the white cells, no operators are specified so a minus sign could only be a prefix. See how the different cases above are
parsed in the video below. It's all about the value used with the
second operator. Is it the adjacent cell or the number following?Which is Which Video |
| Graphics While the charts and graphs in T/Maker are not on a par with well-established spreadsheets, you can use them to get insights into your data and a student can learn what type of chart best illustrates a certain point. This is one of a number of areas where T/Maker could be improved by teaming up with a company that already has a professional collection of charts and graphs. The current graph interface could be kept pretty much as is in terms of simplicity. Better to forgo a few capabilities then start to make things complicated.
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| Forms With four different line styles plus the possibility of no line, you can design some nice forms. Allow text to span multiple columns when setting formats (Alignment "+" Spans). Text can be specified in an invisible ink format effectively blanking it out. This is useful when elements in a table are needed for calculations but not desired in a final print-out. A respectably looking result is achievable with some experience.  This video shows doing a few calculations, changing some formats, adding some lines, and making a graph. You can see the similarity of the approaches to the vaious tasks. Just wartching it might be enough to do an invoice or the like yourself. Video |
Printing Print the table in one of four fonts. Choose font style and size. Set a row height to tighten or spread out the vertical dimension. Decide whether or not to print lines. Options are available for row names and column names. Switch between landscape and portrait as well as set margins with two system dialog boxes called up with a button. The top of the page shows the length and width of your table in pages. In addition to marign adjustments, changing the size of the font and other items may affect these numbers. Use the Recalculate button to refigure the size when you have altered any items. I generally try for a minimum number of pages with the width of only a single page.  |
 StatisticsAlgebra is often a prerequisite for a number of subjects. Some teachers may be thinking that a knowledge of it is necessary to calculate and understand the topic. But T/Maker changes that. A single ampersand cursor running down a column can yield a number of measures for the values included. The difference between the mean and median is "must know" material. Trails have been added here to normalize the data and step up to calculating the correlation coefficients. You can see the temperature scales of Fahrenheit and Centigrade produce the maximum possible value of one. A little explanation of what that coefficient impies could be interesting. And the zero correlation (not shown) between the sine and cosine or easier examples (the same curve but out of phase) might suggest the statistic is not as clever as it can appear to be. Interesting oservations are fun. With the pressure off to become an expert, a basic understanding of stuff can be attractive. Practical geometry was introduced above. Imagine a course with a new topic covered every week and where T/Maker sits on every desk to do the supporting math in real time. Wouldn't that be cool? |
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