Publicly, the 64-year-old is being recognised quite frequently these days, perhaps from the exposure that comes with travelling nation-wide to lead and promote the Evonne Goolagong Foundation for indigenous children. But there was also the woman who kept staring and staring at the well-known face one day until finally blurting out, "Do you work at Coles?" To which the amused former world No.1 replied: "No, but I spend a lot of time there."

Even the students at the schools she visits often have to research her background online before she and husband Roger Cawley arrive to do their thing. "These days I just say 'Google me'. Roger said last night, 'You could say they should Google-gong you'," Goolagong laughs. "And that doesn't matter, because I tell my story."

Others are, clearly, far more controversial. When Fairfax Media sat down with Goolagong Cawley recently, it was while Nick Kyrgios  was amassing a smorgasbord of Wimbledon headlines that continued in Australia and eventually embroiled swimming legend Dawn Fraser through her "go back to where their fathers or parents came from" comment.

Like so many, Goolagong Cawley is an avowed admirer of the 20-year-old's tennis, but less enthused about aspects of his behaviour on court. "He's a great talent, he's got great hands, he's a great athlete, he's got flair, and in that way it's magical to actually watch him, and it's about time we saw someone like that. He can be a great champion, really," she says.

"I just don't agree with the way he's handling himself on the court, really. It's bad manners, basically. I don't like it, and I don't think it represents tennis in Australia very well. He needs to grow up a little bit."

The grandmother of two believes chair umpires should have more control over players misbehaving, due to the example it sets. "Maybe we should have tougher rules. I don't know," she said. "But for (Kyrgios) to become a true champion, I think you have to learn those lessons."

Goolagong Cawley's foundation has adopted her personal mantra of "Dream, Believe, Learn, Achieve". Committed to using tennis as a vehicle to improve indigenous children's education and health, with sport as the carrot and the requirement to attend school and lessons the stick, she is proud of the 43 scholarships provided and the 11 students currently being helped to attend university.

Naturally, with so many talented Aboriginal boys drawn like moths to the football codes, it would be nice, too, to unearth the next tennis champion. Tellingly, to the question of whether there will ever be another like her, "there was Ashleigh", is Goolagong Cawley's swift response. Ash Barty: the young Queenslander who won junior Wimbledon  at 15, made three senior grand slam doubles finals, and then, late last year, took an indefinite break from the game. Her father, Robert, texts the occasional update to the Cawleys, who are keen to support, but not intrude.

"She'll work things out herself," says Noosa-based Goolagong. "I'm just more of a friend and a mentor and I just hope that Ashleigh finds out in herself what she really wants to do with her life, and, most importantly, be happy. She needed the time off, and maybe it's time she needs for herself at the moment. She hasn't really called and asked for any help. I'd be happy to help. I just wish her the best of luck."

Yet if Barty's retreat has served to emphasise the far superior depth of talent in Australia's emerging men at present, then Margaret Court still owns the all-time record for grand slam singles titles – 24 – in the women's game globally. The trouble is that Serena Williams is closing, with her sixth Wimbledon title the 33-year-old American's 21st major overall.

"She's a great champion. I don't see her stopping for a while yet, the way she's going," says Goolagong Cawley. "She's so strong, and a great competitor, a true professional. I think there's a good chance she will probably catch (Court)."

Is that a good thing? "I'd like to keep it in Australia. I want my friend Margaret to keep it, thank you! It would be nice for Australia to keep that record, but I think it's going to be threatened."

Goolagong Cawley finished with seven singles slams – four Australian Opens, two Wimbledons and one French – and finds humour in the fact that a Trivial Pursuit question asks which two players have lost four US Open finals. The other is Bjorn Borg. "But I did it better than him," she laughs. "I was consistent. I did my four in a row."

The second, the 1974 loss to Billie Jean King, felt like a victory, she recalls, because such was the quality and variety of the grasscourt tennis that after one exceptional rally, the Australian noticed goosebumps on her arm. More recently, Goolagong Cawley's "really weird" recurring vision is of chasing down a lob, then whipping back a low backhand crosscourt from barely ankle height. "It's just lately," she shrugs. "I don't know why."

She may never learn, but remains committed to providing more important lessons for others. "Wimbledon reminds me of achieving my first dream," says Goolagong Cawley. "And at the moment I'm living my second dream of working with indigenous kids all around Australia to create better education and health."