There have been complaints that some schools have been allocated between three and five interns while others have received none.
The new Competency-Based Curriculum (CBC) requires a school to have at least six teachers to be able to handle the 12 core learning areas with additional two optional subjects.
"Majority of teachers posted by TSC here are those having a cluster of history and CRE with other learning areas needing outsourcing," said a head teacher who spoke on condition of anonymity.
Many head teachers have identified teachers with diploma and degrees to step in as they await solutions from the Ministry of Education.
For example at Kariobangi South Primary School, though TSC has posted three interns, the management has identified four teachers to handle JSS classes.
"Last week, we received three interns from TSC. The school administration also identified four more teachers from our staff who had up-scaled their education to teach in our JSS section," said Pamela Mang'oli, the head teacher.
At Nairobi School, head teacher Munyau Mbondo is facing a similar problem.
"We realised that some of our teachers had upgraded their academic papers to either diplomas or degree level. We have identified eight of them and elevated them to our junior secondary," Mbondo said.
Kenya Primary Schools Heads Association national chairman Johnson Nzioka said as much as the government is trying to mitigate the problem, much more needs to be done.
"The interns hired by TSC are not enough to fill the gaps in the 24,000 public primary schools across the country. We are experiencing a lot of challenges as a result of teacher shortages," said Nzioka.
Kenya Union Post Primary Education Teachers (Kuppet) secretary general Akelo Misori said schools head are suffering in silence over the shortages.
"We are in a serious crisis that requires a series of consultative meetings with stakeholders to get out of the woods. They may be silent but they are going through a lot of challenges administering these schools," Misori said.