Generalist primary school computer science (CS) teachers are often reluctant to introduce CS activities that go beyond CS unplugged tasks. To address this challenge, we drew from constructive alignment principles to implement a new programming modality for primary school: the handwriting programming language (HPL). HPL brings programming activities closer to existing teaching practices by enabling students to write instructions on paper, take a picture, and have an agent execute them. HPL's applicability in classrooms was investigated in two stages. First, 49 primary school teachers evaluated two alternative programming modalities--HPL and an equivalent paper-based Tangible Programming Language--using the technology acceptance model (TAM). As teachers preferred HPL, we then conducted a 3-session quasi-experimental study with 143 public school students (aged 9-10) to compare HPL's acceptance (with the TAM) and learning outcomes (with a validated test) to the established Scratch programming language. The findings indicate that: (i) over 80% of teachers were willing to use HPL to teach CS in class, irrespective of gender or prior experience; (ii) HPL-students exhibited less trial-and-error behaviour than Scratch-students (fewer attempts, more time between attempts); (iii) students perceived HPL as positively as Scratch; (iv) HPL-students learned as much as Scratch-students. In conclusion, HPL is an accessible, accepted, and pedagogically meaningful means of teaching CS that is as efficient as Scratch to teach CS in primary school. HPL's efficiency and acceptance by teachers and students suggests that handwriting-based programming languages may help shift primary school CS teaching practices, and make CS education more widespread, bringing us closer to CS for all.