Address Book Address Card adjust align-center align-justify align-left align-right Allergies ambulance American Sign Language Interpreting Anchor Angle Double Down Angle Double Left Angle Double Right Angle Double Up angle-down angle-left angle-right angle-up Archive Alternate Arrow Circle Down Alternate Arrow Circle Left Alternate Arrow Circle Right Alternate Arrow Circle Up Arrow Circle Down Arrow Circle Left Arrow Circle Right Arrow Circle Up arrow-down arrow-left arrow-right arrow-up Alternate Arrows Alternate Arrows Horizontal Alternate Arrows Vertical Assistive Listening Systems asterisk At Audio Description backward Balance Scale ban Band-Aid barcode Bars Baseball Ball Basketball Ball Bath Battery Empty Battery Full Battery 1/2 Full Battery 1/4 Full Battery 3/4 Full Bed beer bell Bell Slash Bicycle Binoculars Birthday Cake Blind bold Lightning Bolt Bomb book bookmark Bowling Ball Box Box Open Boxes Braille Briefcase Medical Briefcase Bug Building bullhorn Bullseye Burn Bus Calculator Calendar Alternate Calendar Calendar Check Calendar Minus Calendar Plus Calendar Times camera Retro Camera Capsules Car Caret Down Caret Left Caret Right Caret Square Down Caret Square Left Caret Square Right Caret Square Up Caret Up Shopping Cart Arrow Down Add to Shopping Cart certificate Area Chart Bar Chart Line Chart Pie Chart Check Check Circle Check Square Chess Chess Bishop Chess Board Chess King Chess Knight Chess Pawn Chess Queen Chess Rook Chevron Circle Down Chevron Circle Left Chevron Circle Right Chevron Circle Up chevron-down chevron-left chevron-right chevron-up Child Circle Circle Notched Clipboard Clipboard Check Clipboard List Clock Clone Closed Captioning Cloud Cloud Download Alternate Cloud Upload Alternate Code Code Branch Coffee cog cogs Columns comment Alternate Comment Comment Dots Comment Slash comments Compass Compress Copy Copyright Couch Credit Card crop Crosshairs Cube Cubes Cut Database Deaf Desktop Diagnoses DNA Dollar Sign Dolly Dolly Flatbed Dot Circle Dove Download Edit eject Horizontal Ellipsis Vertical Ellipsis Envelope Envelope Open Envelope Square eraser Euro Sign Alternate Exchange exclamation Exclamation Circle Exclamation Triangle Expand Alternate Expand Arrows Alternate External Link Alternate External Link Square Eye Eye Dropper Eye Slash fast-backward fast-forward Fax Female fighter-jet File Alternate File Archive File Audio File Code File Excel File Image File Medical File Medical File Alternate PDF File Powerpoint File Video File Word File Film Filter fire fire-extinguisher First Aid flag flag-checkered Flask Folder Folder Open font Football Ball forward Frown Futbol Gamepad Gavel Gem Genderless gift Martini Glass Globe Golf Ball Graduation Cap H Square Hand Holding Hand Holding Heart Hand Holding US Dollar Lizard (Hand) Paper (Hand) Peace (Hand) Hand Pointing Down Hand Pointing Left Hand Pointing Right Hand Pointing Up Pointer (Hand) Rock (Hand) Scissors (Hand) Spock (Hand) Hands Helping Hands Handshake Hashtag HDD heading headphones Heart Heartbeat History Hockey Puck home hospital Hospital Alternate Hospital Symbol Hourglass Hourglass End Hourglass Half Hourglass Start I Beam Cursor Identification Badge Identification Card Identification Card Alternate Image Images inbox Indent Industry Info Info Circle italic key Keyboard Language Laptop leaf Lemon Level Down Alternate Level Up Alternate Life Ring Lightbulb Link Turkish Lira Sign List List Alternate list-ol list-ul location-arrow lock Lock Open Alternate Long Arrow Down Alternate Long Arrow Left Alternate Long Arrow Right Alternate Long Arrow Up Low Vision magic magnet Male Map map-marker Map Marker Alternate Map Pin Map Signs Mars Mars Double Mars Stroke Mars Stroke Horizontal Mars Stroke Vertical medkit Meh Mercury Microchip microphone Microphone Slash minus Minus Circle Minus Square Mobile Phone Alternate Mobile Money Bill Alternate Moon Motorcycle Mouse Pointer Music Neuter Newspaper Medical Notes Object Group Object Ungroup Outdent Paint Brush Pallet Paper Plane Paperclip Parachute Box paragraph Paste pause Pause Circle Paw Pen Square Alternate Pencil People Carry Percent Phone Phone Slash Phone Square Phone Volume Piggy Bank Pills plane play Play Circle Plug plus Plus Circle Plus Square Podcast Poo Pound Sign Power Off Prescription Bottle Alternate Prescription Bottle print Procedures Puzzle Piece qrcode Question Question Circle Quidditch quote-left quote-right random Recycle Redo Alternate Redo Registered Trademark Reply reply-all Retweet Ribbon road rocket rss RSS Square Ruble Sign Indian Rupee Sign Save Search Search Minus Search Plus Seedling Server Share Alternate Share Alternate Share Square Share Square Shekel Sign Alternate Shield Ship Shipping Fast Shopping Bag Shopping Basket shopping-cart Shower Sign Alternate Sign In Sign Language Alternate Sign Out signal Sitemap Horizontal Sliders Smile Smoking Snowflake Sort Sort Alpha Down Sort Alpha Up Sort Amount Down Sort Amount Up Sort Down (Descending) Sort Numeric Down Sort Numeric Up Sort Up (Ascending) Space Shuttle Spinner Square Square Full Star star-half step-backward step-forward Stethoscope Sticky Note stop Stop Circle Stopwatch Street View Strikethrough subscript Subway Suitcase Sun superscript Sync Alternate Sync Syringe table Table Tennis tablet Alternate Tablet Tablets Alternate Tachometer tag tags Tape Tasks Taxi Terminal text-height text-width th th-large th-list Thermometer Thermometer Empty Thermometer Full Thermometer 1/2 Full Thermometer 1/4 Full Thermometer 3/4 Full thumbs-down thumbs-up Thumbtack Alternate Ticket Times Times Circle tint Toggle Off Toggle On Trademark Train Transgender Alternate Transgender Trash Alternate Trash Tree trophy truck Truck Loading Truck Moving TTY Television Umbrella Underline Undo Alternate Undo Universal Access University unlink unlock Alternate Unlock Upload User User Circle user-md Add User User Secret Remove User Users Utensil Spoon Utensils Venus Venus Double Venus Mars Vial Vials Video Video Slash Volleyball Ball volume-down volume-off volume-up Warehouse Weight Wheelchair WiFi Window Close Window Maximize Window Minimize Window Restore Wine Glass Won Sign Wrench X-Ray Yen Sign

Timed Arithmetic Computation Test

The TACT is a single sheet "paper and pencil" screening test of primary arithmetic procedural skills, suitable for grade levels 3 to 11 and adult. It can be used individually, or as a group test, and is completed without use of a calculator. It is not a "speeded" test as such, but is usually completed within five minutes, and is standardised on that basis. It is a discretionary option to allow the child or adult more time if needed/requested, depending on your purpose. The test may be useful for teachers, psychologists or others without access to a published standardised skills test. Such instruments include the WIAT, WIDE RANGE ACHIEVEMENT TEST, or scales embedded within psycho educational batteries such as the BAS 3 or DAS 3.

PDF icon TACT158.92 KB
PDF icon TACT Manual95.14 KB

The present standardisation is based only a single school sample, with age based norms for full years only from age 8 to 16 years. The children were from high SES families, and the private R-12 school had a strong curriculum focus on explicit numeracy teaching. Sample size in each age level varied from 11 to 67 (mean of 43). The current standardisation only provides mean scores and standard deviation variability within each year level. No systematic analysis of item difficulty scaling was warranted, although item content sequencing is consistent with that in other major commercial tests. The school’s identity remains confidential by legal agreement. Other schools and organisations are welcome to use the TACT as a group test, to develop their own local norms as required, and compare with the present standardisation as needed.

The test may be used diagnostically by identifying individual item errors as a guide to which procedural skills are still not understood, at an individual or group level. TACT also enables age based screening of proficiency that may be suitable for use in diagnosis of learning difficulties, but it does not yield percentiles or standardised scores. A validated commercial test with broader standardisation would be necessary for that purpose, although concurrent validity would be comparable. The TACT could also be administered with use of calculators permitted, to establish children’s functional proficiency in arithmetic concepts. Analysis of errors in the two forms (with/without calculator) may be diagnostically revealing of an individual child’s poor grasp of underlying procedural skills, or broader patterns of misunderstanding evident in group/class data.

Note that incremental performance is linear from age 8 to 13, and "peaks ‘‘ at 13 years, corresponding to the first year of secondary school. It then declines incrementally, by a small margin, from mean of 14.5 to 13.2 across the secondary years, due primarily to the increasing reliance on electronic calculator devices. This developmental pattern parallels that found with speeded mental arithmetic skills in the TRMA. The decline is even more marked over time in many adults, who similarly become more dependent on a calculator, and do not practice or retain their earlier proficiency level. This early decline over time appears to be unique to  basic numeracy skills compared with other literacy or cognitive processing skills. The latter broadly improve incrementally with schooling, and do not plateau or decline till much later, depending on vocational or recreational usage, or cognitive capacity. It is thus difficult to generate valid, generalizable norms for wider usage. The origins of this reversal reflect current teaching/learning practices, not neurological changes, as discussed in the TRMA manual.

© 2022 Gary Childs