The Bangladeshis have yet to win a Test after 26 matches, losing 25 Tests and drawing the other -- against Zimbabwe -- while the Africans have won just seven of the 71 Tests they have played since 1992.
"Bangladesh are a very improved side under Dav Whatmore, but we've been playing good cricket and there's no reason why we shouldn't dominate and win both the test and one-day series," said Streak.
"I hope our guys rise to the occasion for this series, not just when we play the big guns. It's important that we learn to win, and part of that is beating teams like Bangladesh."
This season Zimbabwe played against powerhouses Australia and India in a triangular series, where Streak's team lost seven of their eight matches with the other washed out.
"We were competitive in a few games and we managed to run them to the wire a couple of times, even after losing (batsmen) Craig Wishart and Mark Vermeulen to injuries," Streak said.
"We were disappointed that we couldn't pull off a couple of victories having gotten ourselves into positions where we could have.
"But India and Australia are the two best sides in world cricket, and the guys took a lot of confidence out of the fact that we were able to be competitive with a very young side and missing a couple of guys."
REVERSE ROLES
Streak
"They'll be asked to play under the sort of pressure we were under against India and Australia," Streak said.
Zimbabwe's all rounders and middle order, Streak said, had become assets to his team.
"We've got some good all rounders, and that allows us to have bowling options," Streak said. "Our middle order has managed to pull us out of trouble and to put us in strong positions.
"We've got guys like (Andy) Blignaut and (Ray) Price coming in at nine and 10 respectively, and they are by no means monkeys with the bat."
Streak was hopeful that Blignaut, an aggressive but often reckless batsman, would have a memorable series.
"If he knuckles down, Blignaut is capable of scoring centuries against guys like Bangladesh," Streak said.
Squads:
Zimbabwe: Heath Streak (captain), Andy Blignaut, Stuart Carlisle, Dion Ebrahim, Sean Ervine, Gavin Ewing, Grant Flower, Trevor Gripper, Douglas Hondo, Blessing Mahwire, Stuart Matsikenyeri, Raymond Price, Tatenda Taibu.
Bangladesh: Habibul Bashar (captain), Mohammad Ashraful, Tareq Aziz, Tapash Baisya, Anwar Hossain, Shahriar Hossain, Manjural Islam, Alamgir Kabir, Alok Kapali, Khaled Mashud, Mohammad Rafique, Mushfiqur Rahman, Rajin Saleh, Al Sahariar, Hannan Sarkar.