After seeing how glass ceilings were shattered and racial stereotypes overcome in the early 1960s, audiences will be cheering for the three courageous, intelligent and classy women featured in the new film “Hidden Figures.”

The film opens by introducing us to Katherine (Lidya Jewett), a young African-American girl who can visualize geometric image from designs contained in stained glass windows. Eventually, Katherine graduates from high school at 14 and from college at 18 in 1937. The film then skips to her first marriage in1939 and her husband’s death in 1959 before fast forwarding to three professionally dressed women with a broken down car on the side of a lonely road in Virginia in 1961. They are: Katherine (now played by Taraji P. Henson), who is widowed with three young daughters; her work supervisor Dorothy Vaughan (Octavia Spencer), who is tinkering under the car’s hood; and their co-worker Mary Jackson (Janelle Monáe).

When a white cop comes by and asks for their identification, he’s surprised to learn, “There are quite a few women working on the space program.” Out of a sense of patriotism for the men in the space program, he offers to give them an escort to NASA’s Langley Research Center. As Mary notes, “Three negro women are chasing a white policeman down a highway in 1961. That is a God-ordained miracle.”

At work, the women are segregated from white employees and are known as “colored computers” (research mathematicians). As this is the Jim Crow South, the women not only had to use a “colored” water fountain but also a “colored” bathroom. But the discrimination doesn’t stop there. Dorothy has been an acting supervisor for months without the extra pay. When she sees that NASA is about to institute IBM computers, she has to work around the “colored” section of the public library.

While Dorothy sets about educating herself on the new system, Mary becomes interested in wind tunnel experiments which help calculate the forces space capsules must be able to withstand. With the support of her husband Levi (Aldis Hodge), Mary goes to court to gain admittance into all-white, all-male courses in order to become an aerospace engineer.

With Mary and Dorothy as wing women, Katherine meets Lt. Colonel James A. Johnson (Mahershala Ali) and quickly sets him straight about women with glasses. Although “Hidden Figures” touches upon their romance, the main focus is on how Katherine gains the respect of the director of the Space Task Group, Al Harrison (Kevin Costner), the grudging cooperation of head researcher Paul Stafford (Jim Parsons) and the confidence of astronaut John Glenn (Glen Powell).

In Allison Schroeder and Theodore Melfi’s screenplay, and under Melfi direction, heavy issues of segregation are dealt with lightly, without bitterness or anger. Pharrell Williams’ upbeat music helps set the tone. Audiences will sympathize with poor Katherine’s half-mile trek across the NASA campus to the colored bathroom until the final confrontation with Harrison. The goal-oriented Harrison takes a baseball bat to the colored bathroom sign, not for any reasons of social equality but because he needs Katherine to work as fast as possible instead of taking an hour for bathroom breaks.

While all three women broke glass ceilings, historically John Glenn asked specifically for Katherine to double check the calculations of the IBM computer, a system that had only recently been introduced into the space program. Remember, by April 1961, the Soviets had already put the first man in space (Yuri Gagarin).  Glenn’s Friendship 7 mission in February 1962 was catchup and his journey back to earth experienced a few scary moments, but his success was a breakthrough for the US space program.

There is some literary license in the movie. Virginia-born Margot Lee Shetterly wrote the 2014 book of the same name on which the film is based. Shetterly’s father worked at the NASA Langley Research Center. Shetterly founded the Human Computer Project in 2013 as a record of female research mathematicians for NASA. According to the Human Computer Project website, when NACA (National Advisory Committee for Aeronautics) transitioned to NASA, segregated facilities were abolished in 1958 (and not in 1961, as portrayed in the movie).

The movie doesn’t follow the women past Glenn’s flight into space, but provides a short epilogue showing what they looked like in real life and briefly what they went on to accomplish.

Only Johnson is still alive. Vaughan died in 2008. Jackson preceded her in death in 2005.

“Hidden Figures” provides a positive image of women as science researchers who were able to balance their personal and professional lives to achieve success.

“Hidden Figures” opens in select theaters on Christmas Day but rolls out nationwide on Jan. 6.