The 10 teenagers, from Coltness High School and St Aidan's High School in Wishaw, North Lanarkshire, will each drag 35kg of equipment across the ice and camp out under the Northern Lights. They are likely to see Arctic foxes, ski on sea ice, cross mountains that have yet to be named and meet Inuit people in hunting villages.
Mathieson, 45, the Royal Scottish Geographical Society's explorer-in-residence who is currently in Greenland making preparations for the trip next April, said it was "really difficult" to choose the 10 children for his Polar Academy out of 19 who went on two selection weekends at Glenmore Lodge outdoor centre near Aviemore, but he picked those he felt would benefit most from the experience.
The Polar Academy has been set up by Mathieson specifically for what he calls "invisible" pupils - not high achievers and sports stars, and not disruptive children for whom there are other initiatives, but the "forgotten" ones in the middle who are shy and lacking in confidence. He himself was such a child. He said: "When I told the 10 who had been selected, I invited them in one by one and all 10 thought they were going to be told no. These kids have never been given a yes before.
"There's an underlying toughness with these kids. Every day they see school as surviving."
He added that some of the children, who will be aged 15-17 when they go to Greenland, show "absolute greatness" but have no idea of their potential. Those who have not been selected will still be trained, ready to step in if an expedition member has to drop out. The nine reserves will do outdoor leadership training at Glenmore and remain an active part of the Polar Academy.
The pupils who have been picked for the expedition are Carla Brawley, Sara Dunn, Morgan Healy, Jack Inglis, Colin Myles, Paul Shuttleworth, Holly Stewart, Jodie Thorburn, Matteusz Trojnar and Rhiannon Walker.
Each expedition member will be set a personal fitness plan by Mathieson. While they do not have to be extremely fit, they must be able to cope with the rigours of dragging their kit a total distance of 60 miles and have the energy at the end of each trek to set up camp and enjoy the evening.
Mathieson, a former tax accountant, now works full time on the project and is sponsored by Norwegian outdoor gear manufacturer Bergans which has a history of supporting explorers.
As well as reaching the South Pole in 2004, the father-of-three and former Royal Navy seaman, who saw active service in the first Gulf War, has been to the North Pole. He decided he wanted to be a polar explorer at the age of 12.
There are polar bears in Greenland but the likelihood of encountering one is very slim. Even so, Mathieson and his team of four, which will include an expedition doctor, will ensure the camp is like Fort Knox, with trip wires, laser fences, drones scanning the surrounding area, people on watch and, as a last resort, rifles.
But he added that the expedition is still "struggling for money", in spite of the support of Bergans, which is providing a lot of kit including clothing, Tiso outdoor shops and North Lanarkshire Council. The expedition requires £50,000 to cover its costs.
He said: "This will be a true life-changing expedition for these kids, they will return to Scotland with a new confidence, ready to achieve anything they put their minds to."
He believes they will be "truly inspirational role models" who will tell their story to 24,000 other schoolchildren on their return.
Mathieson said: "They will be the proof that anyone can achieve in life with the correct attitude and motivation. This is just the beginning. The Polar Academy will continue to expand, with the aim of inspiring the youth right across Scotland."